1 Γραμμική παλινδρόμηση

Στην παρούσα υποενότητα θα χρησιμοποιήσουμε δεδομένα του OECD για τον αριθμό των γιατρών και των νοσοκόμων ανά χίλιους κατοίκους (βλ. εδώ κι εδώ). Αυτά αποθηκεύτηκαν στα αρχεία doctorsPer1000.csv και nurcesPer1000.csv. Εδώ παραθέτουμε τα 100 πρώτα στοιχεία κάθε πίνακα, για λόγους ταχύτητας εκτέλεσης του κώδικα. Φυσικά, πρώτα διαγράψαμε τις μεταβλητές της προηγούμενης ενότητας:

rm(list = ls())

doctorsPer1000.csv

LOCATION	INDICATOR	SUBJECT	MEASURE	FREQUENCY	TIME	Value	Flag.Codes
AUS	MEDICALDOC	TOT	1000HAB	A	1961	1.13	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1964	1.23	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1965	1.22	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1966	1.23	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1967	1.26	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1968	1.24	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1969	1.26	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1970	1.33	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1971	1.26	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1972	1.38	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1973	1.35	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1974	1.42	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1975	1.48	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1976	1.64	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1977	1.65	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1978	1.85	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1979	1.78	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1980	1.85	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1981	1.86	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1982	1.90	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1983	1.95	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1984	1.83	B
AUS	MEDICALDOC	TOT	1000HAB	A	1985	1.91	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1986	2.01	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1987	2.06	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1988	2.10	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1989	2.14	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1990	2.17	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1991	2.33	B
AUS	MEDICALDOC	TOT	1000HAB	A	1992	2.37	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1993	2.40	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1994	2.44	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1995	2.48	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1996	2.40	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1997	2.40	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1998	2.40	NA
AUS	MEDICALDOC	TOT	1000HAB	A	1999	2.45	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2000	2.49	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2001	2.56	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2002	2.56	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2003	2.63	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2004	2.71	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2005	2.78	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2006	2.84	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2007	3.01	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2008	3.02	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2009	3.12	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2011	3.32	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2012	3.31	E
AUS	MEDICALDOC	TOT	1000HAB	A	2013	3.37	NA
AUS	MEDICALDOC	TOT	1000HAB	A	2014	3.45	E
AUS	MEDICALDOC	TOT	1000HAB	A	2015	3.51	E
AUS	MEDICALDOC	TOT	1000HAB	A	2016	3.58	E
AUS	MEDICALDOC	TOT	1000HAB	A	2017	3.68	E
AUS	MEDICALDOC	TOT	1000HAB	A	2018	3.75	E
AUS	MEDICALDOC	TOT	1000HAB	A	2019	3.83	E
AUS	MEDICALDOC	TOT	1000HAB	A	2020	3.91	E
AUS	MEDICALDOC	TOT	1000HAB	A	2021	4.02	E
AUT	MEDICALDOC	TOT	1000HAB	A	1960	1.59	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1961	1.58	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1962	1.57	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1963	1.56	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1964	1.56	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1965	1.56	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1966	1.57	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1967	1.58	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1968	1.60	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1969	1.63	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1970	1.67	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1971	1.70	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1972	1.71	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1973	1.76	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1974	1.81	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1975	1.87	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1976	1.95	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1977	2.01	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1978	2.07	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1979	2.14	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1980	2.21	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1981	2.27	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1982	2.33	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1983	2.42	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1984	2.50	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1985	2.57	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1986	2.67	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1987	2.70	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1988	2.80	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1989	2.90	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1990	3.01	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1991	3.09	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1992	3.21	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1993	3.30	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1994	3.41	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1995	3.51	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1996	3.58	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1997	3.66	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1998	3.77	NA
AUT	MEDICALDOC	TOT	1000HAB	A	1999	3.77	NA
AUT	MEDICALDOC	TOT	1000HAB	A	2000	3.85	NA
AUT	MEDICALDOC	TOT	1000HAB	A	2001	3.96	NA

nurcesPer1000.csv

LOCATION	INDICATOR	SUBJECT	MEASURE	FREQUENCY	TIME	Value	Flag.Codes
AUS	NURSE	TOT	1000HAB	A	1980	10.33	NA
AUS	NURSE	TOT	1000HAB	A	1981	9.91	NA
AUS	NURSE	TOT	1000HAB	A	1982	9.85	NA
AUS	NURSE	TOT	1000HAB	A	1983	9.87	NA
AUS	NURSE	TOT	1000HAB	A	1984	9.91	NA
AUS	NURSE	TOT	1000HAB	A	1985	9.55	NA
AUS	NURSE	TOT	1000HAB	A	1986	10.92	B
AUS	NURSE	TOT	1000HAB	A	1987	11.37	NA
AUS	NURSE	TOT	1000HAB	A	1988	11.60	NA
AUS	NURSE	TOT	1000HAB	A	1989	11.72	NA
AUS	NURSE	TOT	1000HAB	A	1990	11.63	NA
AUS	NURSE	TOT	1000HAB	A	1991	12.08	NA
AUS	NURSE	TOT	1000HAB	A	1992	11.57	NA
AUS	NURSE	TOT	1000HAB	A	1993	11.10	B
AUS	NURSE	TOT	1000HAB	A	1994	11.50	NA
AUS	NURSE	TOT	1000HAB	A	1995	10.84	NA
AUS	NURSE	TOT	1000HAB	A	1996	10.83	NA
AUS	NURSE	TOT	1000HAB	A	1997	10.41	B
AUS	NURSE	TOT	1000HAB	A	1998	10.30	NA
AUS	NURSE	TOT	1000HAB	A	1999	10.17	NA
AUS	NURSE	TOT	1000HAB	A	2000	10.07	NA
AUS	NURSE	TOT	1000HAB	A	2001	9.95	NA
AUS	NURSE	TOT	1000HAB	A	2002	9.94	NA
AUS	NURSE	TOT	1000HAB	A	2003	9.94	NA
AUS	NURSE	TOT	1000HAB	A	2004	10.21	NA
AUS	NURSE	TOT	1000HAB	A	2005	9.76	NA
AUS	NURSE	TOT	1000HAB	A	2007	10.20	NA
AUS	NURSE	TOT	1000HAB	A	2008	10.30	NA
AUS	NURSE	TOT	1000HAB	A	2009	10.18	NA
AUS	NURSE	TOT	1000HAB	A	2011	10.19	NA
AUS	NURSE	TOT	1000HAB	A	2012	10.22	E
AUS	NURSE	TOT	1000HAB	A	2013	11.12	NA
AUS	NURSE	TOT	1000HAB	A	2014	11.28	E
AUS	NURSE	TOT	1000HAB	A	2015	11.39	E
AUS	NURSE	TOT	1000HAB	A	2016	11.57	E
AUS	NURSE	TOT	1000HAB	A	2017	11.69	E
AUS	NURSE	TOT	1000HAB	A	2018	11.93	E
AUS	NURSE	TOT	1000HAB	A	2019	12.23	E
AUS	NURSE	TOT	1000HAB	A	2020	12.28	E
AUS	NURSE	TOT	1000HAB	A	2021	12.81	E
AUT	NURSE	TOT	1000HAB	A	1985	3.41	D
AUT	NURSE	TOT	1000HAB	A	1986	3.56	D
AUT	NURSE	TOT	1000HAB	A	1987	3.69	D
AUT	NURSE	TOT	1000HAB	A	1988	3.67	D
AUT	NURSE	TOT	1000HAB	A	1989	3.82	D
AUT	NURSE	TOT	1000HAB	A	1990	3.91	D
AUT	NURSE	TOT	1000HAB	A	1991	4.02	D
AUT	NURSE	TOT	1000HAB	A	1992	4.19	D
AUT	NURSE	TOT	1000HAB	A	1993	4.43	D
AUT	NURSE	TOT	1000HAB	A	1994	4.75	D
AUT	NURSE	TOT	1000HAB	A	1995	4.95	D
AUT	NURSE	TOT	1000HAB	A	1996	5.06	D
AUT	NURSE	TOT	1000HAB	A	1997	5.19	D
AUT	NURSE	TOT	1000HAB	A	1998	5.27	D
AUT	NURSE	TOT	1000HAB	A	1999	5.42	D
AUT	NURSE	TOT	1000HAB	A	2000	5.55	D
AUT	NURSE	TOT	1000HAB	A	2001	5.58	D
AUT	NURSE	TOT	1000HAB	A	2002	5.68	D
AUT	NURSE	TOT	1000HAB	A	2003	5.68	D
AUT	NURSE	TOT	1000HAB	A	2004	5.93	D
AUT	NURSE	TOT	1000HAB	A	2005	5.99	D
AUT	NURSE	TOT	1000HAB	A	2006	6.14	D
AUT	NURSE	TOT	1000HAB	A	2007	6.21	D
AUT	NURSE	TOT	1000HAB	A	2008	6.36	D
AUT	NURSE	TOT	1000HAB	A	2009	6.47	D
AUT	NURSE	TOT	1000HAB	A	2010	6.53	D
AUT	NURSE	TOT	1000HAB	A	2011	6.62	D
AUT	NURSE	TOT	1000HAB	A	2012	6.65	D
AUT	NURSE	TOT	1000HAB	A	2013	6.69	D
AUT	NURSE	TOT	1000HAB	A	2014	6.79	D
AUT	NURSE	TOT	1000HAB	A	2015	6.80	D
AUT	NURSE	TOT	1000HAB	A	2016	6.77	D
AUT	NURSE	TOT	1000HAB	A	2017	6.85	D
AUT	NURSE	TOT	1000HAB	A	2018	6.85	D
AUT	NURSE	TOT	1000HAB	A	2019	10.30	B
AUT	NURSE	TOT	1000HAB	A	2020	10.32	NA
AUT	NURSE	TOT	1000HAB	A	2021	10.60	NA
CAN	NURSE	TOT	1000HAB	A	2003	8.51	NA
CAN	NURSE	TOT	1000HAB	A	2004	8.51	NA
CAN	NURSE	TOT	1000HAB	A	2005	8.73	NA
CAN	NURSE	TOT	1000HAB	A	2006	8.84	NA
CAN	NURSE	TOT	1000HAB	A	2007	9.04	NA
CAN	NURSE	TOT	1000HAB	A	2008	9.16	NA
CAN	NURSE	TOT	1000HAB	A	2009	9.32	NA
CAN	NURSE	TOT	1000HAB	A	2010	9.37	NA
CAN	NURSE	TOT	1000HAB	A	2011	9.29	NA
CAN	NURSE	TOT	1000HAB	A	2012	9.40	NA
CAN	NURSE	TOT	1000HAB	A	2013	9.54	NA
CAN	NURSE	TOT	1000HAB	A	2014	9.81	NA
CAN	NURSE	TOT	1000HAB	A	2015	9.91	NA
CAN	NURSE	TOT	1000HAB	A	2016	9.96	NA
CAN	NURSE	TOT	1000HAB	A	2017	10.00	NA
CAN	NURSE	TOT	1000HAB	A	2018	9.95	NA
CAN	NURSE	TOT	1000HAB	A	2019	9.98	NA
CAN	NURSE	TOT	1000HAB	A	2020	10.06	NA
CAN	NURSE	TOT	1000HAB	A	2021	10.25	NA
CZE	NURSE	TOT	1000HAB	A	1980	5.95	NA
CZE	NURSE	TOT	1000HAB	A	1981	6.09	NA
CZE	NURSE	TOT	1000HAB	A	1982	6.26	NA
CZE	NURSE	TOT	1000HAB	A	1983	6.41	NA

Αυτά ενοποιήθηκαν, κατά τα γνωστά (βλ. υποενότητα «Συγχώνευση πινάκων δίπλα-δίπλα» της Προσθήκη στοιχείων σε πίνακα), γράφοντας:

DocNurc <- merge(doctorsPer1000,nurcesPer1000,by=c("LOCATION","TIME"))

LOCATION	TIME	INDICATOR.x	SUBJECT.x	MEASURE.x	FREQUENCY.x	Value.x	Flag.Codes.x	INDICATOR.y	SUBJECT.y	MEASURE.y	FREQUENCY.y	Value.y	Flag.Codes.y
AUS	1980	MEDICALDOC	TOT	1000HAB	A	1.85	NA	NURSE	TOT	1000HAB	A	10.33	NA
AUS	1981	MEDICALDOC	TOT	1000HAB	A	1.86	NA	NURSE	TOT	1000HAB	A	9.91	NA
AUS	1982	MEDICALDOC	TOT	1000HAB	A	1.90	NA	NURSE	TOT	1000HAB	A	9.85	NA
AUS	1983	MEDICALDOC	TOT	1000HAB	A	1.95	NA	NURSE	TOT	1000HAB	A	9.87	NA
AUS	1984	MEDICALDOC	TOT	1000HAB	A	1.83	B	NURSE	TOT	1000HAB	A	9.91	NA
AUS	1985	MEDICALDOC	TOT	1000HAB	A	1.91	NA	NURSE	TOT	1000HAB	A	9.55	NA
AUS	1986	MEDICALDOC	TOT	1000HAB	A	2.01	NA	NURSE	TOT	1000HAB	A	10.92	B
AUS	1987	MEDICALDOC	TOT	1000HAB	A	2.06	NA	NURSE	TOT	1000HAB	A	11.37	NA
AUS	1988	MEDICALDOC	TOT	1000HAB	A	2.10	NA	NURSE	TOT	1000HAB	A	11.60	NA
AUS	1989	MEDICALDOC	TOT	1000HAB	A	2.14	NA	NURSE	TOT	1000HAB	A	11.72	NA
AUS	1990	MEDICALDOC	TOT	1000HAB	A	2.17	NA	NURSE	TOT	1000HAB	A	11.63	NA
AUS	1991	MEDICALDOC	TOT	1000HAB	A	2.33	B	NURSE	TOT	1000HAB	A	12.08	NA
AUS	1992	MEDICALDOC	TOT	1000HAB	A	2.37	NA	NURSE	TOT	1000HAB	A	11.57	NA
AUS	1993	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	11.10	B
AUS	1994	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	11.50	NA
AUS	1995	MEDICALDOC	TOT	1000HAB	A	2.48	NA	NURSE	TOT	1000HAB	A	10.84	NA
AUS	1996	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.83	NA
AUS	1997	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.41	B
AUS	1998	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.30	NA
AUS	1999	MEDICALDOC	TOT	1000HAB	A	2.45	NA	NURSE	TOT	1000HAB	A	10.17	NA
AUS	2000	MEDICALDOC	TOT	1000HAB	A	2.49	NA	NURSE	TOT	1000HAB	A	10.07	NA
AUS	2001	MEDICALDOC	TOT	1000HAB	A	2.56	NA	NURSE	TOT	1000HAB	A	9.95	NA
AUS	2002	MEDICALDOC	TOT	1000HAB	A	2.56	NA	NURSE	TOT	1000HAB	A	9.94	NA
AUS	2003	MEDICALDOC	TOT	1000HAB	A	2.63	NA	NURSE	TOT	1000HAB	A	9.94	NA
AUS	2004	MEDICALDOC	TOT	1000HAB	A	2.71	NA	NURSE	TOT	1000HAB	A	10.21	NA
AUS	2005	MEDICALDOC	TOT	1000HAB	A	2.78	NA	NURSE	TOT	1000HAB	A	9.76	NA
AUS	2007	MEDICALDOC	TOT	1000HAB	A	3.01	NA	NURSE	TOT	1000HAB	A	10.20	NA
AUS	2008	MEDICALDOC	TOT	1000HAB	A	3.02	NA	NURSE	TOT	1000HAB	A	10.30	NA
AUS	2009	MEDICALDOC	TOT	1000HAB	A	3.12	NA	NURSE	TOT	1000HAB	A	10.18	NA
AUS	2011	MEDICALDOC	TOT	1000HAB	A	3.32	NA	NURSE	TOT	1000HAB	A	10.19	NA
AUS	2012	MEDICALDOC	TOT	1000HAB	A	3.31	E	NURSE	TOT	1000HAB	A	10.22	E
AUS	2013	MEDICALDOC	TOT	1000HAB	A	3.37	NA	NURSE	TOT	1000HAB	A	11.12	NA
AUS	2014	MEDICALDOC	TOT	1000HAB	A	3.45	E	NURSE	TOT	1000HAB	A	11.28	E
AUS	2015	MEDICALDOC	TOT	1000HAB	A	3.51	E	NURSE	TOT	1000HAB	A	11.39	E
AUS	2016	MEDICALDOC	TOT	1000HAB	A	3.58	E	NURSE	TOT	1000HAB	A	11.57	E
AUS	2017	MEDICALDOC	TOT	1000HAB	A	3.68	E	NURSE	TOT	1000HAB	A	11.69	E
AUS	2018	MEDICALDOC	TOT	1000HAB	A	3.75	E	NURSE	TOT	1000HAB	A	11.93	E
AUS	2019	MEDICALDOC	TOT	1000HAB	A	3.83	E	NURSE	TOT	1000HAB	A	12.23	E
AUS	2020	MEDICALDOC	TOT	1000HAB	A	3.91	E	NURSE	TOT	1000HAB	A	12.28	E
AUS	2021	MEDICALDOC	TOT	1000HAB	A	4.02	E	NURSE	TOT	1000HAB	A	12.81	E
AUT	1985	MEDICALDOC	TOT	1000HAB	A	2.57	NA	NURSE	TOT	1000HAB	A	3.41	D
AUT	1986	MEDICALDOC	TOT	1000HAB	A	2.67	NA	NURSE	TOT	1000HAB	A	3.56	D
AUT	1987	MEDICALDOC	TOT	1000HAB	A	2.70	NA	NURSE	TOT	1000HAB	A	3.69	D
AUT	1988	MEDICALDOC	TOT	1000HAB	A	2.80	NA	NURSE	TOT	1000HAB	A	3.67	D
AUT	1989	MEDICALDOC	TOT	1000HAB	A	2.90	NA	NURSE	TOT	1000HAB	A	3.82	D
AUT	1990	MEDICALDOC	TOT	1000HAB	A	3.01	NA	NURSE	TOT	1000HAB	A	3.91	D
AUT	1991	MEDICALDOC	TOT	1000HAB	A	3.09	NA	NURSE	TOT	1000HAB	A	4.02	D
AUT	1992	MEDICALDOC	TOT	1000HAB	A	3.21	NA	NURSE	TOT	1000HAB	A	4.19	D
AUT	1993	MEDICALDOC	TOT	1000HAB	A	3.30	NA	NURSE	TOT	1000HAB	A	4.43	D
AUT	1994	MEDICALDOC	TOT	1000HAB	A	3.41	NA	NURSE	TOT	1000HAB	A	4.75	D
AUT	1995	MEDICALDOC	TOT	1000HAB	A	3.51	NA	NURSE	TOT	1000HAB	A	4.95	D
AUT	1996	MEDICALDOC	TOT	1000HAB	A	3.58	NA	NURSE	TOT	1000HAB	A	5.06	D
AUT	1997	MEDICALDOC	TOT	1000HAB	A	3.66	NA	NURSE	TOT	1000HAB	A	5.19	D
AUT	1998	MEDICALDOC	TOT	1000HAB	A	3.77	NA	NURSE	TOT	1000HAB	A	5.27	D
AUT	1999	MEDICALDOC	TOT	1000HAB	A	3.77	NA	NURSE	TOT	1000HAB	A	5.42	D
AUT	2000	MEDICALDOC	TOT	1000HAB	A	3.85	NA	NURSE	TOT	1000HAB	A	5.55	D
AUT	2001	MEDICALDOC	TOT	1000HAB	A	3.96	NA	NURSE	TOT	1000HAB	A	5.58	D
AUT	2002	MEDICALDOC	TOT	1000HAB	A	4.03	NA	NURSE	TOT	1000HAB	A	5.68	D
AUT	2003	MEDICALDOC	TOT	1000HAB	A	4.11	NA	NURSE	TOT	1000HAB	A	5.68	D
AUT	2004	MEDICALDOC	TOT	1000HAB	A	4.20	NA	NURSE	TOT	1000HAB	A	5.93	D
AUT	2005	MEDICALDOC	TOT	1000HAB	A	4.32	NA	NURSE	TOT	1000HAB	A	5.99	D
AUT	2006	MEDICALDOC	TOT	1000HAB	A	4.45	NA	NURSE	TOT	1000HAB	A	6.14	D
AUT	2007	MEDICALDOC	TOT	1000HAB	A	4.52	B	NURSE	TOT	1000HAB	A	6.21	D
AUT	2008	MEDICALDOC	TOT	1000HAB	A	4.59	NA	NURSE	TOT	1000HAB	A	6.36	D
AUT	2009	MEDICALDOC	TOT	1000HAB	A	4.67	NA	NURSE	TOT	1000HAB	A	6.47	D
AUT	2010	MEDICALDOC	TOT	1000HAB	A	4.77	NA	NURSE	TOT	1000HAB	A	6.53	D
AUT	2011	MEDICALDOC	TOT	1000HAB	A	4.82	NA	NURSE	TOT	1000HAB	A	6.62	D
AUT	2012	MEDICALDOC	TOT	1000HAB	A	4.87	NA	NURSE	TOT	1000HAB	A	6.65	D
AUT	2013	MEDICALDOC	TOT	1000HAB	A	4.96	B	NURSE	TOT	1000HAB	A	6.69	D
AUT	2014	MEDICALDOC	TOT	1000HAB	A	5.02	NA	NURSE	TOT	1000HAB	A	6.79	D
AUT	2015	MEDICALDOC	TOT	1000HAB	A	5.06	NA	NURSE	TOT	1000HAB	A	6.80	D
AUT	2016	MEDICALDOC	TOT	1000HAB	A	5.11	NA	NURSE	TOT	1000HAB	A	6.77	D
AUT	2017	MEDICALDOC	TOT	1000HAB	A	5.16	NA	NURSE	TOT	1000HAB	A	6.85	D
AUT	2018	MEDICALDOC	TOT	1000HAB	A	5.22	NA	NURSE	TOT	1000HAB	A	6.85	D
AUT	2019	MEDICALDOC	TOT	1000HAB	A	5.29	NA	NURSE	TOT	1000HAB	A	10.30	B
AUT	2020	MEDICALDOC	TOT	1000HAB	A	5.32	NA	NURSE	TOT	1000HAB	A	10.32	NA
AUT	2021	MEDICALDOC	TOT	1000HAB	A	5.41	NA	NURSE	TOT	1000HAB	A	10.60	NA
BEL	2004	MEDICALDOC	TOT	1000HAB	A	2.87	NA	NURSE	TOT	1000HAB	A	8.79	E
BEL	2005	MEDICALDOC	TOT	1000HAB	A	2.87	NA	NURSE	TOT	1000HAB	A	9.01	E
BEL	2006	MEDICALDOC	TOT	1000HAB	A	2.89	NA	NURSE	TOT	1000HAB	A	9.12	E
BEL	2007	MEDICALDOC	TOT	1000HAB	A	2.91	NA	NURSE	TOT	1000HAB	A	9.24	E
BEL	2008	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.32	E
BEL	2009	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.42	NA
BEL	2010	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.59	E
BEL	2011	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.81	E
BEL	2012	MEDICALDOC	TOT	1000HAB	A	2.93	NA	NURSE	TOT	1000HAB	A	10.02	E
BEL	2013	MEDICALDOC	TOT	1000HAB	A	2.96	NA	NURSE	TOT	1000HAB	A	10.30	E
BEL	2014	MEDICALDOC	TOT	1000HAB	A	2.98	NA	NURSE	TOT	1000HAB	A	10.58	E
BEL	2015	MEDICALDOC	TOT	1000HAB	A	3.02	NA	NURSE	TOT	1000HAB	A	10.83	E
BEL	2016	MEDICALDOC	TOT	1000HAB	A	3.07	NA	NURSE	TOT	1000HAB	A	10.96	B
BEL	2017	MEDICALDOC	TOT	1000HAB	A	3.08	NA	NURSE	TOT	1000HAB	A	11.22	NA
BEL	2018	MEDICALDOC	TOT	1000HAB	A	3.13	NA	NURSE	TOT	1000HAB	A	11.07	NA
BRA	2007	MEDICALDOC	TOT	1000HAB	A	1.30	NA	NURSE	TOT	1000HAB	A	0.50	NA
BRA	2008	MEDICALDOC	TOT	1000HAB	A	1.41	NA	NURSE	TOT	1000HAB	A	0.56	NA
BRA	2009	MEDICALDOC	TOT	1000HAB	A	1.46	NA	NURSE	TOT	1000HAB	A	0.61	NA
BRA	2010	MEDICALDOC	TOT	1000HAB	A	1.52	NA	NURSE	TOT	1000HAB	A	0.67	NA
BRA	2011	MEDICALDOC	TOT	1000HAB	A	1.50	NA	NURSE	TOT	1000HAB	A	0.73	NA
BRA	2012	MEDICALDOC	TOT	1000HAB	A	1.55	NA	NURSE	TOT	1000HAB	A	0.80	NA
BRA	2013	MEDICALDOC	TOT	1000HAB	A	1.62	NA	NURSE	TOT	1000HAB	A	0.88	NA
BRA	2014	MEDICALDOC	TOT	1000HAB	A	1.71	NA	NURSE	TOT	1000HAB	A	0.97	NA

Είναι αναμενόμενο οι αριθμοί των γιατρών ανά χίλιους κατοίκους και οι αριθμοί των νοσοκόμων θα συσχετίζονται με κάποιον τρόπο. Ποιος είναι άραγε αυτός ο τρόπος; Θα ήταν χρήσιμο να έχουμε έναν μαθηματικό τύπο, όπου δίνοντάς του μια τιμή για τον αριθμό των νοσοκόμων (π.χ. 2 νοσοκόμες ανά χίλιους κατοίκους), να μας υπολογίζει τον αριθμό των γιατρών (εν προκειμένω είναι 1.64 γιατροί ανά χίλιους κατοίκους).

Για να κάνουμε ευκολότερη την μελέτη των δύο ομάδων αριθμών, τους δίνουμε ονόματα μέσω της κλασσικής διαδικασίας:

giatroi <- DocNurc$Value.x
nosok <- DocNurc$Value.y

Το να επιδιώξουμε εδώ την απόλυτη ακρίβεια, περισσότερο θα συσκότιζε την εικόνα που θέλουμε ν’ αποκτήσουμε, παρά θα την ξεκαθάριζε. Η απόλυτη ακρίβεια θα ήταν ένας μαθηματικός τύπος, ιδιαίτερα περίπλοκος και ακατάλληλος για εκτιμήσεις σχέσεων, αλλά και υπολογισμούς προβλέψεων. O πιο απλός τύπος θα ήταν μια γραμμική σχέση:

\[[giatroi]=\alpha+\beta\cdot[nosok]\]

η οποία θα εκφράζει στο περίπου τον αριθμό των γιατρών βάσει του αριθμού των νοσοκόμων. Κερδίσαμε κάτι σε απλότητα τύπου, χάσαμε όμως κάτι σε ακρίβεια. Δεν πειράζει, καλή καρδιά.

Πόσο δυνατόν όμως είναι αυτό; Το πλήθος των γιατρών είναι γραμμικώς συσχετισμένο με το πλήθος των νοσοκόμων; Σύμφωνα με όσα έχουμε πει (βλ. ενότητα Συντελεστής γραμμικής συσχέτισης Pearson), γράφουμε:

cor(giatroi,nosok)

## [1] 0.5528042

Βρίσκουμε συντελεστή γραμμικής συσχέτισης Pearson 0.5528042, άρα έχουμε ισχυρή γραμμική συσχέτιση. Επομένως δικαιολογούμαστε να περιμένουμε ότι θα υπάρχει μαθηματικός τύπος σαν τον προηγούμενο που να συνδέει το πλήθος των γιατρών με το πλήθος των νοσοκόμων. Γράφουμε λοιπόν:

lm(giatroi ~ nosok)

## 
## Call:
## lm(formula = giatroi ~ nosok)
## 
## Coefficients:
## (Intercept)        nosok  
##      1.9248       0.1308

Αυτό σημαίνει ότι:

\[[giatroi]=1.9248+0.1308\cdot[nosok]\]

Έτσι, μπορούμε να εικάσουμε πως πχ για 2.23 νοσοκόμους ανά χίλιους κατοίκους, θα έχουμε πιθανότατα κατά μέσο όρο:

\[1.9248+0.1308\cdot2.23=2.216484\]

γιατρούς ανά χίλους κατοίκους.

Ευθεία γραμμικής παλινδρόμησης
Η ευθεία γραμμικής παλινδρόμησης σχεδιάστηκε να προσεγγίζει τις μέσες τιμές ενός μεγέθους (πχ του αριθμού των γιατρών) δεδομένης της εκάστοτε τιμής ενός άλλου μεγέθους (πχ του αριθμού των νοσοκόμων).

Μια σχέση της μορφής \([giatroi]=1.9248+0.1308\cdot[nosok]\) δεν αποκαλείται τυχαία «ευθεία γραμμικής παλινδόμησης», διότι, αν τη σχεδιάσουμε σ’ ένα σύστημα συντεταγμένων (π.χ. εκεί που σχεδιάσαμε το διάγραμμα διασποράς), θα σχηματίσουν τα σημεία μιας ευθείας γραμμής. Για να σχεδιαστεί η εν λόγω ευθεία στην θα χρησιμοποιήσουμε την συνάρτηση abline(). Βέβαια, πριν την σχεδιάσουμε, πρέπει να ’χουμε ήδη φτιαγμένο ένα σύστημα συντεταγμένων, οπότε γράφουμε (βλ. ενότητα Διάγραμμα διασποράς):

plot(giatroi ~ nosok)

Πάνω σ’ αυτό το διάγραμμα διασποράς θα σχεδιαστεί η ευθεία της απλής γραμμικής παλινδρόμησης συμπληρώνοντας από κάτω abline(lm(giatroi ~ nosok), col = "red"), δηλαδή:

plot(giatroi ~ nosok)
abline(lm(giatroi ~ nosok), col = "red")

Εναλλακτικά τα παραπάνω μπορούν να γίνουν μέσω της συνάρτησης geom_smooth() του πακέτου ggplot2 γράφοντας:

if(!require(ggplot2)){
    install.packages("ggplot2")
    library(ggplot2)
}
DocNurcEyth <- ggplot(DocNurc, aes(x = nosok, y = giatroi))
DocNurcEyth + geom_smooth(method='lm')

Αν θέλουμε να είναι μαζί με το διάγραμμα διασποράς, γράφουμε:

DocNurcEyth + geom_point() + geom_smooth(method='lm')

## `geom_smooth()` using formula = 'y ~ x'

Για να δούμε περισσότερες αισθητικές παρεμβάσεις θα χρησιμοποιήσουμε κάποια επιπλέον δεδομένα. Αντλήσαμε από το datahub στοιχεία για τις χώρες και τις ηπείρους που ανήκουν. Τα δεδομένα αποθηκεύτηκαν σ’ ένα αρχείο ονόματι XoresHpiroi2.txt.

Continent_Name	Continent_Code	Country_Name	Two_Letter_Country_Code	Three_Letter_Country_Code	Country_Number
Asia	AS	Afghanistan, Islamic Republic of	AF	AFG	4
Europe	EU	Albania, Republic of	AL	ALB	8
Antarctica	AN	Antarctica (the territory South of 60 deg S)	AQ	ATA	10
Africa	AF	Algeria, People’s Democratic Republic of	DZ	DZA	12
Oceania	OC	American Samoa	AS	ASM	16
Europe	EU	Andorra, Principality of	AD	AND	20
Africa	AF	Angola, Republic of	AO	AGO	24
North America	NA	Antigua and Barbuda	AG	ATG	28
Europe	EU	Azerbaijan, Republic of	AZ	AZE	31
Asia	AS	Azerbaijan, Republic of	AZ	AZE	31
South America	SA	Argentina, Argentine Republic	AR	ARG	32
Oceania	OC	Australia, Commonwealth of	AU	AUS	36
Europe	EU	Austria, Republic of	AT	AUT	40
North America	NA	Bahamas, Commonwealth of the	BS	BHS	44
Asia	AS	Bahrain, Kingdom of	BH	BHR	48
Asia	AS	Bangladesh, People’s Republic of	BD	BGD	50
Europe	EU	Armenia, Republic of	AM	ARM	51
Asia	AS	Armenia, Republic of	AM	ARM	51
North America	NA	Barbados	BB	BRB	52
Europe	EU	Belgium, Kingdom of	BE	BEL	56
North America	NA	Bermuda	BM	BMU	60
Asia	AS	Bhutan, Kingdom of	BT	BTN	64
South America	SA	Bolivia, Republic of	BO	BOL	68
Europe	EU	Bosnia and Herzegovina	BA	BIH	70
Africa	AF	Botswana, Republic of	BW	BWA	72
Antarctica	AN	Bouvet Island (Bouvetoya)	BV	BVT	74
South America	SA	Brazil, Federative Republic of	BR	BRA	76
North America	NA	Belize	BZ	BLZ	84
Asia	AS	British Indian Ocean Territory (Chagos Archipelago)	IO	IOT	86
Oceania	OC	Solomon Islands	SB	SLB	90
North America	NA	British Virgin Islands	VG	VGB	92
Asia	AS	Brunei Darussalam	BN	BRN	96
Europe	EU	Bulgaria, Republic of	BG	BGR	100
Asia	AS	Myanmar, Union of	MM	MMR	104
Africa	AF	Burundi, Republic of	BI	BDI	108
Europe	EU	Belarus, Republic of	BY	BLR	112
Asia	AS	Cambodia, Kingdom of	KH	KHM	116
Africa	AF	Cameroon, Republic of	CM	CMR	120
North America	NA	Canada	CA	CAN	124
Africa	AF	Cape Verde, Republic of	CV	CPV	132
North America	NA	Cayman Islands	KY	CYM	136
Africa	AF	Central African Republic	CF	CAF	140
Asia	AS	Sri Lanka, Democratic Socialist Republic of	LK	LKA	144
Africa	AF	Chad, Republic of	TD	TCD	148
South America	SA	Chile, Republic of	CL	CHL	152
Asia	AS	China, People’s Republic of	CN	CHN	156
Asia	AS	Taiwan	TW	TWN	158
Asia	AS	Christmas Island	CX	CXR	162
Asia	AS	Cocos (Keeling) Islands	CC	CCK	166
South America	SA	Colombia, Republic of	CO	COL	170
Africa	AF	Comoros, Union of the	KM	COM	174
Africa	AF	Mayotte	YT	MYT	175
Africa	AF	Congo, Republic of the	CG	COG	178
Africa	AF	Congo, Democratic Republic of the	CD	COD	180
Oceania	OC	Cook Islands	CK	COK	184
North America	NA	Costa Rica, Republic of	CR	CRI	188
Europe	EU	Croatia, Republic of	HR	HRV	191
North America	NA	Cuba, Republic of	CU	CUB	192
Europe	EU	Cyprus, Republic of	CY	CYP	196
Asia	AS	Cyprus, Republic of	CY	CYP	196
Europe	EU	Czech Republic	CZ	CZE	203
Africa	AF	Benin, Republic of	BJ	BEN	204
Europe	EU	Denmark, Kingdom of	DK	DNK	208
North America	NA	Dominica, Commonwealth of	DM	DMA	212
North America	NA	Dominican Republic	DO	DOM	214
South America	SA	Ecuador, Republic of	EC	ECU	218
North America	NA	El Salvador, Republic of	SV	SLV	222
Africa	AF	Equatorial Guinea, Republic of	GQ	GNQ	226
Africa	AF	Ethiopia, Federal Democratic Republic of	ET	ETH	231
Africa	AF	Eritrea, State of	ER	ERI	232
Europe	EU	Estonia, Republic of	EE	EST	233
Europe	EU	Faroe Islands	FO	FRO	234
South America	SA	Falkland Islands (Malvinas)	FK	FLK	238
Antarctica	AN	South Georgia and the South Sandwich Islands	GS	SGS	239
Oceania	OC	Fiji, Republic of the Fiji Islands	FJ	FJI	242
Europe	EU	Finland, Republic of	FI	FIN	246
Europe	EU	Γland Islands	\|AX	\|ALA	24

Αυτά συνενώθηκαν με τον πίνακα DocNurc γράφοντας πρώτα:

names(XoresHpiroi2)[names(XoresHpiroi2) == "Three_Letter_Country_Code"] <- "LOCATION"

για να μετονομάσουμε την στήλη Three_Letter_Country_Code σε LOCATION

Ακολούθως:

DocNurcCont <- merge(DocNurc,XoresHpiroi2,by = "LOCATION")

LOCATION	TIME	INDICATOR.x	SUBJECT.x	MEASURE.x	FREQUENCY.x	Value.x	Flag.Codes.x	INDICATOR.y	SUBJECT.y	MEASURE.y	FREQUENCY.y	Value.y	Flag.Codes.y	Continent_Name	Continent_Code	Country_Name	Two_Letter_Country_Code	Country_Number
AUS	1980	MEDICALDOC	TOT	1000HAB	A	1.85	NA	NURSE	TOT	1000HAB	A	10.33	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1981	MEDICALDOC	TOT	1000HAB	A	1.86	NA	NURSE	TOT	1000HAB	A	9.91	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1982	MEDICALDOC	TOT	1000HAB	A	1.90	NA	NURSE	TOT	1000HAB	A	9.85	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1983	MEDICALDOC	TOT	1000HAB	A	1.95	NA	NURSE	TOT	1000HAB	A	9.87	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1984	MEDICALDOC	TOT	1000HAB	A	1.83	B	NURSE	TOT	1000HAB	A	9.91	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1985	MEDICALDOC	TOT	1000HAB	A	1.91	NA	NURSE	TOT	1000HAB	A	9.55	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1986	MEDICALDOC	TOT	1000HAB	A	2.01	NA	NURSE	TOT	1000HAB	A	10.92	B	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1987	MEDICALDOC	TOT	1000HAB	A	2.06	NA	NURSE	TOT	1000HAB	A	11.37	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1988	MEDICALDOC	TOT	1000HAB	A	2.10	NA	NURSE	TOT	1000HAB	A	11.60	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1989	MEDICALDOC	TOT	1000HAB	A	2.14	NA	NURSE	TOT	1000HAB	A	11.72	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1990	MEDICALDOC	TOT	1000HAB	A	2.17	NA	NURSE	TOT	1000HAB	A	11.63	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1991	MEDICALDOC	TOT	1000HAB	A	2.33	B	NURSE	TOT	1000HAB	A	12.08	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1992	MEDICALDOC	TOT	1000HAB	A	2.37	NA	NURSE	TOT	1000HAB	A	11.57	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1993	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	11.10	B	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1994	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	11.50	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1995	MEDICALDOC	TOT	1000HAB	A	2.48	NA	NURSE	TOT	1000HAB	A	10.84	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1996	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.83	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1997	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.41	B	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1998	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	10.30	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	1999	MEDICALDOC	TOT	1000HAB	A	2.45	NA	NURSE	TOT	1000HAB	A	10.17	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2000	MEDICALDOC	TOT	1000HAB	A	2.49	NA	NURSE	TOT	1000HAB	A	10.07	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2001	MEDICALDOC	TOT	1000HAB	A	2.56	NA	NURSE	TOT	1000HAB	A	9.95	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2002	MEDICALDOC	TOT	1000HAB	A	2.56	NA	NURSE	TOT	1000HAB	A	9.94	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2003	MEDICALDOC	TOT	1000HAB	A	2.63	NA	NURSE	TOT	1000HAB	A	9.94	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2004	MEDICALDOC	TOT	1000HAB	A	2.71	NA	NURSE	TOT	1000HAB	A	10.21	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2005	MEDICALDOC	TOT	1000HAB	A	2.78	NA	NURSE	TOT	1000HAB	A	9.76	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2007	MEDICALDOC	TOT	1000HAB	A	3.01	NA	NURSE	TOT	1000HAB	A	10.20	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2008	MEDICALDOC	TOT	1000HAB	A	3.02	NA	NURSE	TOT	1000HAB	A	10.30	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2009	MEDICALDOC	TOT	1000HAB	A	3.12	NA	NURSE	TOT	1000HAB	A	10.18	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2011	MEDICALDOC	TOT	1000HAB	A	3.32	NA	NURSE	TOT	1000HAB	A	10.19	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2012	MEDICALDOC	TOT	1000HAB	A	3.31	E	NURSE	TOT	1000HAB	A	10.22	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2013	MEDICALDOC	TOT	1000HAB	A	3.37	NA	NURSE	TOT	1000HAB	A	11.12	NA	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2014	MEDICALDOC	TOT	1000HAB	A	3.45	E	NURSE	TOT	1000HAB	A	11.28	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2015	MEDICALDOC	TOT	1000HAB	A	3.51	E	NURSE	TOT	1000HAB	A	11.39	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2016	MEDICALDOC	TOT	1000HAB	A	3.58	E	NURSE	TOT	1000HAB	A	11.57	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2017	MEDICALDOC	TOT	1000HAB	A	3.68	E	NURSE	TOT	1000HAB	A	11.69	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2018	MEDICALDOC	TOT	1000HAB	A	3.75	E	NURSE	TOT	1000HAB	A	11.93	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2019	MEDICALDOC	TOT	1000HAB	A	3.83	E	NURSE	TOT	1000HAB	A	12.23	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2020	MEDICALDOC	TOT	1000HAB	A	3.91	E	NURSE	TOT	1000HAB	A	12.28	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUS	2021	MEDICALDOC	TOT	1000HAB	A	4.02	E	NURSE	TOT	1000HAB	A	12.81	E	Oceania	OC	Australia, Commonwealth of	AU	36
AUT	1985	MEDICALDOC	TOT	1000HAB	A	2.57	NA	NURSE	TOT	1000HAB	A	3.41	D	Europe	EU	Austria, Republic of	AT	40
AUT	1986	MEDICALDOC	TOT	1000HAB	A	2.67	NA	NURSE	TOT	1000HAB	A	3.56	D	Europe	EU	Austria, Republic of	AT	40
AUT	1987	MEDICALDOC	TOT	1000HAB	A	2.70	NA	NURSE	TOT	1000HAB	A	3.69	D	Europe	EU	Austria, Republic of	AT	40
AUT	1988	MEDICALDOC	TOT	1000HAB	A	2.80	NA	NURSE	TOT	1000HAB	A	3.67	D	Europe	EU	Austria, Republic of	AT	40
AUT	1989	MEDICALDOC	TOT	1000HAB	A	2.90	NA	NURSE	TOT	1000HAB	A	3.82	D	Europe	EU	Austria, Republic of	AT	40
AUT	1990	MEDICALDOC	TOT	1000HAB	A	3.01	NA	NURSE	TOT	1000HAB	A	3.91	D	Europe	EU	Austria, Republic of	AT	40
AUT	1991	MEDICALDOC	TOT	1000HAB	A	3.09	NA	NURSE	TOT	1000HAB	A	4.02	D	Europe	EU	Austria, Republic of	AT	40
AUT	1992	MEDICALDOC	TOT	1000HAB	A	3.21	NA	NURSE	TOT	1000HAB	A	4.19	D	Europe	EU	Austria, Republic of	AT	40
AUT	1993	MEDICALDOC	TOT	1000HAB	A	3.30	NA	NURSE	TOT	1000HAB	A	4.43	D	Europe	EU	Austria, Republic of	AT	40
AUT	1994	MEDICALDOC	TOT	1000HAB	A	3.41	NA	NURSE	TOT	1000HAB	A	4.75	D	Europe	EU	Austria, Republic of	AT	40
AUT	1995	MEDICALDOC	TOT	1000HAB	A	3.51	NA	NURSE	TOT	1000HAB	A	4.95	D	Europe	EU	Austria, Republic of	AT	40
AUT	1996	MEDICALDOC	TOT	1000HAB	A	3.58	NA	NURSE	TOT	1000HAB	A	5.06	D	Europe	EU	Austria, Republic of	AT	40
AUT	1997	MEDICALDOC	TOT	1000HAB	A	3.66	NA	NURSE	TOT	1000HAB	A	5.19	D	Europe	EU	Austria, Republic of	AT	40
AUT	1998	MEDICALDOC	TOT	1000HAB	A	3.77	NA	NURSE	TOT	1000HAB	A	5.27	D	Europe	EU	Austria, Republic of	AT	40
AUT	1999	MEDICALDOC	TOT	1000HAB	A	3.77	NA	NURSE	TOT	1000HAB	A	5.42	D	Europe	EU	Austria, Republic of	AT	40
AUT	2000	MEDICALDOC	TOT	1000HAB	A	3.85	NA	NURSE	TOT	1000HAB	A	5.55	D	Europe	EU	Austria, Republic of	AT	40
AUT	2001	MEDICALDOC	TOT	1000HAB	A	3.96	NA	NURSE	TOT	1000HAB	A	5.58	D	Europe	EU	Austria, Republic of	AT	40
AUT	2002	MEDICALDOC	TOT	1000HAB	A	4.03	NA	NURSE	TOT	1000HAB	A	5.68	D	Europe	EU	Austria, Republic of	AT	40
AUT	2003	MEDICALDOC	TOT	1000HAB	A	4.11	NA	NURSE	TOT	1000HAB	A	5.68	D	Europe	EU	Austria, Republic of	AT	40
AUT	2004	MEDICALDOC	TOT	1000HAB	A	4.20	NA	NURSE	TOT	1000HAB	A	5.93	D	Europe	EU	Austria, Republic of	AT	40
AUT	2005	MEDICALDOC	TOT	1000HAB	A	4.32	NA	NURSE	TOT	1000HAB	A	5.99	D	Europe	EU	Austria, Republic of	AT	40
AUT	2006	MEDICALDOC	TOT	1000HAB	A	4.45	NA	NURSE	TOT	1000HAB	A	6.14	D	Europe	EU	Austria, Republic of	AT	40
AUT	2007	MEDICALDOC	TOT	1000HAB	A	4.52	B	NURSE	TOT	1000HAB	A	6.21	D	Europe	EU	Austria, Republic of	AT	40
AUT	2008	MEDICALDOC	TOT	1000HAB	A	4.59	NA	NURSE	TOT	1000HAB	A	6.36	D	Europe	EU	Austria, Republic of	AT	40
AUT	2009	MEDICALDOC	TOT	1000HAB	A	4.67	NA	NURSE	TOT	1000HAB	A	6.47	D	Europe	EU	Austria, Republic of	AT	40
AUT	2010	MEDICALDOC	TOT	1000HAB	A	4.77	NA	NURSE	TOT	1000HAB	A	6.53	D	Europe	EU	Austria, Republic of	AT	40
AUT	2011	MEDICALDOC	TOT	1000HAB	A	4.82	NA	NURSE	TOT	1000HAB	A	6.62	D	Europe	EU	Austria, Republic of	AT	40
AUT	2012	MEDICALDOC	TOT	1000HAB	A	4.87	NA	NURSE	TOT	1000HAB	A	6.65	D	Europe	EU	Austria, Republic of	AT	40
AUT	2013	MEDICALDOC	TOT	1000HAB	A	4.96	B	NURSE	TOT	1000HAB	A	6.69	D	Europe	EU	Austria, Republic of	AT	40
AUT	2014	MEDICALDOC	TOT	1000HAB	A	5.02	NA	NURSE	TOT	1000HAB	A	6.79	D	Europe	EU	Austria, Republic of	AT	40
AUT	2015	MEDICALDOC	TOT	1000HAB	A	5.06	NA	NURSE	TOT	1000HAB	A	6.80	D	Europe	EU	Austria, Republic of	AT	40
AUT	2016	MEDICALDOC	TOT	1000HAB	A	5.11	NA	NURSE	TOT	1000HAB	A	6.77	D	Europe	EU	Austria, Republic of	AT	40
AUT	2017	MEDICALDOC	TOT	1000HAB	A	5.16	NA	NURSE	TOT	1000HAB	A	6.85	D	Europe	EU	Austria, Republic of	AT	40
AUT	2018	MEDICALDOC	TOT	1000HAB	A	5.22	NA	NURSE	TOT	1000HAB	A	6.85	D	Europe	EU	Austria, Republic of	AT	40
AUT	2019	MEDICALDOC	TOT	1000HAB	A	5.29	NA	NURSE	TOT	1000HAB	A	10.30	B	Europe	EU	Austria, Republic of	AT	40
AUT	2020	MEDICALDOC	TOT	1000HAB	A	5.32	NA	NURSE	TOT	1000HAB	A	10.32	NA	Europe	EU	Austria, Republic of	AT	40
AUT	2021	MEDICALDOC	TOT	1000HAB	A	5.41	NA	NURSE	TOT	1000HAB	A	10.60	NA	Europe	EU	Austria, Republic of	AT	40
BEL	2004	MEDICALDOC	TOT	1000HAB	A	2.87	NA	NURSE	TOT	1000HAB	A	8.79	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2005	MEDICALDOC	TOT	1000HAB	A	2.87	NA	NURSE	TOT	1000HAB	A	9.01	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2006	MEDICALDOC	TOT	1000HAB	A	2.89	NA	NURSE	TOT	1000HAB	A	9.12	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2007	MEDICALDOC	TOT	1000HAB	A	2.91	NA	NURSE	TOT	1000HAB	A	9.24	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2008	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.32	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2009	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.42	NA	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2010	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.59	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2011	MEDICALDOC	TOT	1000HAB	A	2.92	NA	NURSE	TOT	1000HAB	A	9.81	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2012	MEDICALDOC	TOT	1000HAB	A	2.93	NA	NURSE	TOT	1000HAB	A	10.02	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2013	MEDICALDOC	TOT	1000HAB	A	2.96	NA	NURSE	TOT	1000HAB	A	10.30	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2014	MEDICALDOC	TOT	1000HAB	A	2.98	NA	NURSE	TOT	1000HAB	A	10.58	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2015	MEDICALDOC	TOT	1000HAB	A	3.02	NA	NURSE	TOT	1000HAB	A	10.83	E	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2016	MEDICALDOC	TOT	1000HAB	A	3.07	NA	NURSE	TOT	1000HAB	A	10.96	B	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2017	MEDICALDOC	TOT	1000HAB	A	3.08	NA	NURSE	TOT	1000HAB	A	11.22	NA	Europe	EU	Belgium, Kingdom of	BE	56
BEL	2018	MEDICALDOC	TOT	1000HAB	A	3.13	NA	NURSE	TOT	1000HAB	A	11.07	NA	Europe	EU	Belgium, Kingdom of	BE	56
BRA	2007	MEDICALDOC	TOT	1000HAB	A	1.30	NA	NURSE	TOT	1000HAB	A	0.50	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2008	MEDICALDOC	TOT	1000HAB	A	1.41	NA	NURSE	TOT	1000HAB	A	0.56	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2009	MEDICALDOC	TOT	1000HAB	A	1.46	NA	NURSE	TOT	1000HAB	A	0.61	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2010	MEDICALDOC	TOT	1000HAB	A	1.52	NA	NURSE	TOT	1000HAB	A	0.67	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2011	MEDICALDOC	TOT	1000HAB	A	1.50	NA	NURSE	TOT	1000HAB	A	0.73	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2012	MEDICALDOC	TOT	1000HAB	A	1.55	NA	NURSE	TOT	1000HAB	A	0.80	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2013	MEDICALDOC	TOT	1000HAB	A	1.62	NA	NURSE	TOT	1000HAB	A	0.88	NA	South America	SA	Brazil, Federative Republic of	BR	76
BRA	2014	MEDICALDOC	TOT	1000HAB	A	1.71	NA	NURSE	TOT	1000HAB	A	0.97	NA	South America	SA	Brazil, Federative Republic of	BR	76

Κατόπιν από αυτόν τον πίνακα κρατήσαμε τις χώρες της Βορείου Αμερικής, γράφοντας:

DocNurcAm <- DocNurcCont[DocNurcCont$Continent_Name == "South America" | DocNurcCont$Continent_Name == "North America", ]

	LOCATION	TIME	INDICATOR.x	SUBJECT.x	MEASURE.x	FREQUENCY.x	Value.x	Flag.Codes.x	INDICATOR.y	SUBJECT.y	MEASURE.y	FREQUENCY.y	Value.y	Flag.Codes.y	Continent_Name	Continent_Code	Country_Name	Two_Letter_Country_Code	Country_Number
93	BRA	2007	MEDICALDOC	TOT	1000HAB	A	1.30	NA	NURSE	TOT	1000HAB	A	0.50	NA	South America	SA	Brazil, Federative Republic of	BR	76
94	BRA	2008	MEDICALDOC	TOT	1000HAB	A	1.41	NA	NURSE	TOT	1000HAB	A	0.56	NA	South America	SA	Brazil, Federative Republic of	BR	76
95	BRA	2009	MEDICALDOC	TOT	1000HAB	A	1.46	NA	NURSE	TOT	1000HAB	A	0.61	NA	South America	SA	Brazil, Federative Republic of	BR	76
96	BRA	2010	MEDICALDOC	TOT	1000HAB	A	1.52	NA	NURSE	TOT	1000HAB	A	0.67	NA	South America	SA	Brazil, Federative Republic of	BR	76
97	BRA	2011	MEDICALDOC	TOT	1000HAB	A	1.50	NA	NURSE	TOT	1000HAB	A	0.73	NA	South America	SA	Brazil, Federative Republic of	BR	76
98	BRA	2012	MEDICALDOC	TOT	1000HAB	A	1.55	NA	NURSE	TOT	1000HAB	A	0.80	NA	South America	SA	Brazil, Federative Republic of	BR	76
99	BRA	2013	MEDICALDOC	TOT	1000HAB	A	1.62	NA	NURSE	TOT	1000HAB	A	0.88	NA	South America	SA	Brazil, Federative Republic of	BR	76
100	BRA	2014	MEDICALDOC	TOT	1000HAB	A	1.71	NA	NURSE	TOT	1000HAB	A	0.97	NA	South America	SA	Brazil, Federative Republic of	BR	76
101	BRA	2015	MEDICALDOC	TOT	1000HAB	A	1.73	NA	NURSE	TOT	1000HAB	A	1.03	NA	South America	SA	Brazil, Federative Republic of	BR	76
102	BRA	2016	MEDICALDOC	TOT	1000HAB	A	1.79	NA	NURSE	TOT	1000HAB	A	1.08	NA	South America	SA	Brazil, Federative Republic of	BR	76
103	BRA	2017	MEDICALDOC	TOT	1000HAB	A	1.86	NA	NURSE	TOT	1000HAB	A	1.14	NA	South America	SA	Brazil, Federative Republic of	BR	76
104	BRA	2018	MEDICALDOC	TOT	1000HAB	A	1.90	NA	NURSE	TOT	1000HAB	A	1.21	NA	South America	SA	Brazil, Federative Republic of	BR	76
105	BRA	2019	MEDICALDOC	TOT	1000HAB	A	1.97	NA	NURSE	TOT	1000HAB	A	1.27	NA	South America	SA	Brazil, Federative Republic of	BR	76
106	BRA	2020	MEDICALDOC	TOT	1000HAB	A	2.05	NA	NURSE	TOT	1000HAB	A	1.42	NA	South America	SA	Brazil, Federative Republic of	BR	76
107	BRA	2021	MEDICALDOC	TOT	1000HAB	A	2.15	NA	NURSE	TOT	1000HAB	A	1.55	NA	South America	SA	Brazil, Federative Republic of	BR	76
108	CAN	2003	MEDICALDOC	TOT	1000HAB	A	2.10	NA	NURSE	TOT	1000HAB	A	8.51	NA	North America	NA	Canada	CA	124
109	CAN	2004	MEDICALDOC	TOT	1000HAB	A	2.13	NA	NURSE	TOT	1000HAB	A	8.51	NA	North America	NA	Canada	CA	124
110	CAN	2005	MEDICALDOC	TOT	1000HAB	A	2.16	NA	NURSE	TOT	1000HAB	A	8.73	NA	North America	NA	Canada	CA	124
111	CAN	2006	MEDICALDOC	TOT	1000HAB	A	2.18	NA	NURSE	TOT	1000HAB	A	8.84	NA	North America	NA	Canada	CA	124
112	CAN	2007	MEDICALDOC	TOT	1000HAB	A	2.22	NA	NURSE	TOT	1000HAB	A	9.04	NA	North America	NA	Canada	CA	124
113	CAN	2008	MEDICALDOC	TOT	1000HAB	A	2.26	NA	NURSE	TOT	1000HAB	A	9.16	NA	North America	NA	Canada	CA	124
114	CAN	2009	MEDICALDOC	TOT	1000HAB	A	2.34	NA	NURSE	TOT	1000HAB	A	9.32	NA	North America	NA	Canada	CA	124
115	CAN	2010	MEDICALDOC	TOT	1000HAB	A	2.38	NA	NURSE	TOT	1000HAB	A	9.37	NA	North America	NA	Canada	CA	124
116	CAN	2011	MEDICALDOC	TOT	1000HAB	A	2.46	NA	NURSE	TOT	1000HAB	A	9.29	NA	North America	NA	Canada	CA	124
117	CAN	2012	MEDICALDOC	TOT	1000HAB	A	2.51	NA	NURSE	TOT	1000HAB	A	9.40	NA	North America	NA	Canada	CA	124
118	CAN	2013	MEDICALDOC	TOT	1000HAB	A	2.57	NA	NURSE	TOT	1000HAB	A	9.54	NA	North America	NA	Canada	CA	124
119	CAN	2014	MEDICALDOC	TOT	1000HAB	A	2.62	NA	NURSE	TOT	1000HAB	A	9.81	NA	North America	NA	Canada	CA	124
120	CAN	2015	MEDICALDOC	TOT	1000HAB	A	2.67	NA	NURSE	TOT	1000HAB	A	9.91	NA	North America	NA	Canada	CA	124
121	CAN	2016	MEDICALDOC	TOT	1000HAB	A	2.69	NA	NURSE	TOT	1000HAB	A	9.96	NA	North America	NA	Canada	CA	124
122	CAN	2017	MEDICALDOC	TOT	1000HAB	A	2.73	NA	NURSE	TOT	1000HAB	A	10.00	NA	North America	NA	Canada	CA	124
123	CAN	2018	MEDICALDOC	TOT	1000HAB	A	2.78	NA	NURSE	TOT	1000HAB	A	9.95	NA	North America	NA	Canada	CA	124
124	CAN	2019	MEDICALDOC	TOT	1000HAB	A	2.78	NA	NURSE	TOT	1000HAB	A	9.98	NA	North America	NA	Canada	CA	124
125	CAN	2020	MEDICALDOC	TOT	1000HAB	A	2.77	NA	NURSE	TOT	1000HAB	A	10.06	NA	North America	NA	Canada	CA	124
126	CAN	2021	MEDICALDOC	TOT	1000HAB	A	2.81	E	NURSE	TOT	1000HAB	A	10.25	NA	North America	NA	Canada	CA	124
665	MEX	1990	MEDICALDOC	TOT	1000HAB	A	0.97	NA	NURSE	TOT	1000HAB	A	1.75	NA	North America	NA	Mexico, United Mexican States	MX	484
666	MEX	1991	MEDICALDOC	TOT	1000HAB	A	1.16	NA	NURSE	TOT	1000HAB	A	1.89	NA	North America	NA	Mexico, United Mexican States	MX	484
667	MEX	1992	MEDICALDOC	TOT	1000HAB	A	1.31	NA	NURSE	TOT	1000HAB	A	1.99	NA	North America	NA	Mexico, United Mexican States	MX	484
668	MEX	1993	MEDICALDOC	TOT	1000HAB	A	1.46	NA	NURSE	TOT	1000HAB	A	2.03	NA	North America	NA	Mexico, United Mexican States	MX	484
669	MEX	1994	MEDICALDOC	TOT	1000HAB	A	1.56	NA	NURSE	TOT	1000HAB	A	2.09	NA	North America	NA	Mexico, United Mexican States	MX	484
670	MEX	1995	MEDICALDOC	TOT	1000HAB	A	1.65	NA	NURSE	TOT	1000HAB	A	2.13	NA	North America	NA	Mexico, United Mexican States	MX	484
671	MEX	1996	MEDICALDOC	TOT	1000HAB	A	1.65	NA	NURSE	TOT	1000HAB	A	2.12	NA	North America	NA	Mexico, United Mexican States	MX	484
672	MEX	1997	MEDICALDOC	TOT	1000HAB	A	1.69	NA	NURSE	TOT	1000HAB	A	2.10	NA	North America	NA	Mexico, United Mexican States	MX	484
673	MEX	1998	MEDICALDOC	TOT	1000HAB	A	1.71	NA	NURSE	TOT	1000HAB	A	2.14	NA	North America	NA	Mexico, United Mexican States	MX	484
674	MEX	1999	MEDICALDOC	TOT	1000HAB	A	1.71	NA	NURSE	TOT	1000HAB	A	2.19	NA	North America	NA	Mexico, United Mexican States	MX	484
675	MEX	2000	MEDICALDOC	TOT	1000HAB	A	1.63	NA	NURSE	TOT	1000HAB	A	2.23	NA	North America	NA	Mexico, United Mexican States	MX	484
676	MEX	2001	MEDICALDOC	TOT	1000HAB	A	1.52	NA	NURSE	TOT	1000HAB	A	2.23	NA	North America	NA	Mexico, United Mexican States	MX	484
677	MEX	2002	MEDICALDOC	TOT	1000HAB	A	1.53	NA	NURSE	TOT	1000HAB	A	2.23	NA	North America	NA	Mexico, United Mexican States	MX	484
678	MEX	2003	MEDICALDOC	TOT	1000HAB	A	1.58	NA	NURSE	TOT	1000HAB	A	2.14	NA	North America	NA	Mexico, United Mexican States	MX	484
679	MEX	2004	MEDICALDOC	TOT	1000HAB	A	1.66	NA	NURSE	TOT	1000HAB	A	2.12	NA	North America	NA	Mexico, United Mexican States	MX	484
680	MEX	2005	MEDICALDOC	TOT	1000HAB	A	1.77	NA	NURSE	TOT	1000HAB	A	2.21	NA	North America	NA	Mexico, United Mexican States	MX	484
681	MEX	2006	MEDICALDOC	TOT	1000HAB	A	1.89	NA	NURSE	TOT	1000HAB	A	2.23	NA	North America	NA	Mexico, United Mexican States	MX	484
682	MEX	2007	MEDICALDOC	TOT	1000HAB	A	1.93	NA	NURSE	TOT	1000HAB	A	2.29	NA	North America	NA	Mexico, United Mexican States	MX	484
683	MEX	2008	MEDICALDOC	TOT	1000HAB	A	1.96	NA	NURSE	TOT	1000HAB	A	2.32	NA	North America	NA	Mexico, United Mexican States	MX	484
684	MEX	2009	MEDICALDOC	TOT	1000HAB	A	1.99	NA	NURSE	TOT	1000HAB	A	2.37	NA	North America	NA	Mexico, United Mexican States	MX	484
685	MEX	2010	MEDICALDOC	TOT	1000HAB	A	2.00	NA	NURSE	TOT	1000HAB	A	2.42	NA	North America	NA	Mexico, United Mexican States	MX	484
686	MEX	2011	MEDICALDOC	TOT	1000HAB	A	2.11	NA	NURSE	TOT	1000HAB	A	2.52	NA	North America	NA	Mexico, United Mexican States	MX	484
687	MEX	2012	MEDICALDOC	TOT	1000HAB	A	2.12	NA	NURSE	TOT	1000HAB	A	2.56	NA	North America	NA	Mexico, United Mexican States	MX	484
688	MEX	2013	MEDICALDOC	TOT	1000HAB	A	2.16	NA	NURSE	TOT	1000HAB	A	2.62	NA	North America	NA	Mexico, United Mexican States	MX	484
689	MEX	2014	MEDICALDOC	TOT	1000HAB	A	2.23	NA	NURSE	TOT	1000HAB	A	2.69	NA	North America	NA	Mexico, United Mexican States	MX	484
690	MEX	2015	MEDICALDOC	TOT	1000HAB	A	2.33	NA	NURSE	TOT	1000HAB	A	2.77	NA	North America	NA	Mexico, United Mexican States	MX	484
691	MEX	2016	MEDICALDOC	TOT	1000HAB	A	2.34	NA	NURSE	TOT	1000HAB	A	2.87	NA	North America	NA	Mexico, United Mexican States	MX	484
692	MEX	2017	MEDICALDOC	TOT	1000HAB	A	2.40	NA	NURSE	TOT	1000HAB	A	2.87	NA	North America	NA	Mexico, United Mexican States	MX	484
693	MEX	2018	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	2.87	NA	North America	NA	Mexico, United Mexican States	MX	484
694	MEX	2019	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	2.85	NA	North America	NA	Mexico, United Mexican States	MX	484
695	MEX	2020	MEDICALDOC	TOT	1000HAB	A	2.41	NA	NURSE	TOT	1000HAB	A	2.91	NA	North America	NA	Mexico, United Mexican States	MX	484
696	MEX	2021	MEDICALDOC	TOT	1000HAB	A	2.51	NA	NURSE	TOT	1000HAB	A	2.94	NA	North America	NA	Mexico, United Mexican States	MX	484
976	USA	1999	MEDICALDOC	TOT	1000HAB	A	2.24	NA	NURSE	TOT	1000HAB	A	10.37	NA	North America	NA	United States of America	US	840
977	USA	2000	MEDICALDOC	TOT	1000HAB	A	2.29	NA	NURSE	TOT	1000HAB	A	10.17	NA	North America	NA	United States of America	US	840
978	USA	2001	MEDICALDOC	TOT	1000HAB	A	2.35	NA	NURSE	TOT	1000HAB	A	10.18	NA	North America	NA	United States of America	US	840
979	USA	2002	MEDICALDOC	TOT	1000HAB	A	2.35	NA	NURSE	TOT	1000HAB	A	10.19	NA	North America	NA	United States of America	US	840
980	USA	2003	MEDICALDOC	TOT	1000HAB	A	2.38	NA	NURSE	TOT	1000HAB	A	10.10	NA	North America	NA	United States of America	US	840
981	USA	2004	MEDICALDOC	TOT	1000HAB	A	2.39	NA	NURSE	TOT	1000HAB	A	10.30	NA	North America	NA	United States of America	US	840
982	USA	2005	MEDICALDOC	TOT	1000HAB	A	2.43	NA	NURSE	TOT	1000HAB	A	10.42	NA	North America	NA	United States of America	US	840
983	USA	2006	MEDICALDOC	TOT	1000HAB	A	2.42	NA	NURSE	TOT	1000HAB	A	10.52	NA	North America	NA	United States of America	US	840
984	USA	2007	MEDICALDOC	TOT	1000HAB	A	2.43	NA	NURSE	TOT	1000HAB	A	10.58	NA	North America	NA	United States of America	US	840
985	USA	2008	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	10.76	NA	North America	NA	United States of America	US	840
986	USA	2009	MEDICALDOC	TOT	1000HAB	A	2.44	NA	NURSE	TOT	1000HAB	A	10.80	NA	North America	NA	United States of America	US	840
987	USA	2010	MEDICALDOC	TOT	1000HAB	A	2.43	NA	NURSE	TOT	1000HAB	A	10.94	NA	North America	NA	United States of America	US	840
988	USA	2011	MEDICALDOC	TOT	1000HAB	A	2.46	NA	NURSE	TOT	1000HAB	A	11.08	NA	North America	NA	United States of America	US	840
989	USA	2012	MEDICALDOC	TOT	1000HAB	A	2.50	NA	NURSE	TOT	1000HAB	A	11.15	NA	North America	NA	United States of America	US	840
990	USA	2013	MEDICALDOC	TOT	1000HAB	A	2.56	NA	NURSE	TOT	1000HAB	A	11.14	NA	North America	NA	United States of America	US	840
991	USA	2014	MEDICALDOC	TOT	1000HAB	A	2.58	NA	NURSE	TOT	1000HAB	A	11.18	NA	North America	NA	United States of America	US	840
992	USA	2015	MEDICALDOC	TOT	1000HAB	A	2.58	NA	NURSE	TOT	1000HAB	A	11.31	NA	North America	NA	United States of America	US	840
993	USA	2016	MEDICALDOC	TOT	1000HAB	A	2.59	NA	NURSE	TOT	1000HAB	A	11.63	NA	North America	NA	United States of America	US	840
994	USA	2017	MEDICALDOC	TOT	1000HAB	A	2.61	NA	NURSE	TOT	1000HAB	A	11.76	NA	North America	NA	United States of America	US	840
995	USA	2018	MEDICALDOC	TOT	1000HAB	A	2.61	NA	NURSE	TOT	1000HAB	A	11.88	NA	North America	NA	United States of America	US	840
996	USA	2019	MEDICALDOC	TOT	1000HAB	A	2.64	NA	NURSE	TOT	1000HAB	A	11.97	NA	North America	NA	United States of America	US	840
997	USA	2020	MEDICALDOC	TOT	1000HAB	A	2.63	NA	NURSE	TOT	1000HAB	A	11.83	B	North America	NA	United States of America	US	840
998	USA	2021	MEDICALDOC	TOT	1000HAB	A	2.67	NA	NURSE	TOT	1000HAB	A	11.98	NA	North America	NA	United States of America	US	840

Έτσι γράφουμε:

DocNurcEythAm <- ggplot(DocNurcAm, aes(x = Value.y, y = Value.x, color=LOCATION))
DocNurcEythAm + geom_point() + geom_smooth(method='lm')

## `geom_smooth()` using formula = 'y ~ x'

Έτσι έχουμε τις ευθείες γραμμικής παλινδρόμησης για κάθε χώρα της Βορείου Αμερικής. Παρατηρούμε την έντονη γραμμική σύνδεση γιατρών-νοσοκόμων σε κάθε χώρα. Ίσως η κοινή ύπαρξη ευθειών ευθείες να αντικατοπτρίζει μια κοινή προσέγγιση στο σύστημα υγείας, η οποία να εξειδικεύεται διαφορετικά σε κάθε περίπτωση, εξ ου και οι διαφορετικές ευθείες.

1.1 Τυπικό σφάλμα εκτίμησης

Προφανώς, η σχέση \([giatroi]=1.9248+0.1308\cdot[nosok]\) κάνει μια εκτίμηση του αριθμού των γιατρών, δεδομένου του αριθμού των νοσοκόμων. Δεν δίνει ακριβή τιμή για το πλήθος των γιατρών. Συνεπώς θα θέλαμε να ξέρουμε πόσο έξω πέφτει η πρόβλεψή μας από την πραγματικότητα. Αυτή τη δουλειά την κάνει το τυπικό σφάλμα εκτίμησης, και για να υπολογιστεί αυτό στην R γράφουμε:

GramGiatNos <- lm(giatroi ~ nosok)
summary(GramGiatNos)

## 
## Call:
## lm(formula = giatroi ~ nosok)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.86940 -0.60321 -0.08686  0.57112  2.39898 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.924824   0.055397   34.75   <2e-16 ***
## nosok       0.130831   0.006399   20.45   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.815 on 950 degrees of freedom
## Multiple R-squared:  0.3056, Adjusted R-squared:  0.3049 
## F-statistic: 418.1 on 1 and 950 DF,  p-value: < 2.2e-16

οπότε παίρνουμε την απάντηση Residual standard error: 0.815. Αυτό σημαίνει ότι (βλ. και ενότητα Απομονωμένα σημεία) ότι σχεδόν όλες οι μετρήσεις (περίπου το 88.8%) θα είναι σε απόσταση \(\pm 3\cdot 0.815\) από αυτήν που προβλέπει η ευθεία γραμμικής παλινδρόμησης.

2 Ποσοστημοριακή παλινδρόμηση

Δυστυχώς, η ευθεία γραμμικής παλινδρόμησης είναι αρκετά ευαίσθητη στα απομονωμένα σημεία. Η ύπαρξη αρκετών τέτοιων μειώνει πολύ την περιγραφική της δύναμη. Γι’ αυτό το λόγο έχουμε και μια άλλη ευθεία. Την ευθεία ποσοστημοριακής παλινδρόμησης.

Ευθεία ποσοστημοριακής παλινδρόμησης
Η ευθεία ποσοστημοριακής παλινδρόμησης σχεδιάστηκε να προσεγγίζει τις διαμέσους ενός μεγέθους (πχ του αριθμού των γιατρών) δεδομένης της εκάστοτε τιμής ενός άλλου μεγέθους (πχ του αριθμού των νοσοκόμων).

Για να πετύχουμε αυτό το στόχο στην R, θα χρησιμοποιήσουμε το πακέτο quantreg γράφοντας:

if(!require(quantreg)){
    install.packages("quantreg")
    library(quantreg)
}

και ακολούθως:

rq(giatroi ~ nosok)

## Call:
## rq(formula = giatroi ~ nosok)
## 
## Coefficients:
## (Intercept)       nosok 
##   1.6962080   0.1466408 
## 
## Degrees of freedom: 952 total; 950 residual

δηλαδή ότι:

\[[giatroi]=1.6962080+0.1466408\cdot[nosok]\]

Το ίδιο μπορούμε να κάνουμε και με άλλα μέτρα θέσης, συγγενικά προς την διάμεσο, τα ποσοστημόρια (βλ. ενότητα Τεταρτημόρια – Ποσοστημόρια). Θέλοντας μία ευθεία που να προσεγγίζει π.χ. το 0.15-ποσοστημόριο μπορούμε να συμπληρώσουμε την παράμετρο tau=, δηλαδή γράφουμε:

rq(giatroi ~ nosok, tau = 0.15)

## Call:
## rq(formula = giatroi ~ nosok, tau = 0.15)
## 
## Coefficients:
## (Intercept)       nosok 
##   1.0584211   0.1342642 
## 
## Degrees of freedom: 952 total; 950 residual

δηλαδή αν πχ έχουμε 2.23 νοσοκόμους ανά χίλιους κατοίκους, τότε υπολογίζοντας

\[1.0584211+ 0.1342642\cdot2.23=1.35783\]

βρίσκουμε ότι κάτω από 1.35783 γιατροί ανά χίλιους κατοίκους είναι στο χαμηλότερο 15% αυτών που αντιστοιχούν στους 2.23 νοσοκόμους.

Οι σχέσεις:

\[[giatroi]=1.6962080+0.1466408\cdot[nosok]\]

\[[giatroi]=1.0584211+ 0.1342642\cdot[nosok]\]

που βρήκαμε γράφουμε, ονομάζονται ποσοστημοριακές γραμμικές παρεμβολές για τ=0.5 (tau=0.5) και τ=0.15 (tau=0.15) αντίστοιχα. Για να σχεδιάσουμε τις ευθείες ποσοστημοριακής παλινδρόμησης όπως και πριν γράφουμε:

plot(giatroi ~ nosok) 
abline(rq(giatroi ~ nosok), col="red")
abline(rq(giatroi ~ nosok, tau = 0.15), col="blue")

Συνολικά ο κώδικας που γράψαμε είναι ο:

rm(list = ls())
DocNurc <- merge(doctorsPer1000,nurcesPer1000,by=c("LOCATION","TIME"))
giatroi <- DocNurc$Value.x
nosok <- DocNurc$Value.y
cor(giatroi,nosok)
lm(giatroi ~ nosok)
plot(giatroi ~ nosok)
abline(lm(giatroi ~ nosok), col = "red")
if(!require(ggplot2)){
    install.packages("ggplot2")
    library(ggplot2)
}
DocNurcEyth <- ggplot(DocNurc, aes(x = nosok, y = giatroi))
DocNurcEyth + geom_smooth(method='lm')
DocNurcEyth + geom_point() + geom_smooth(method='lm')
names(XoresHpiroi2)[names(XoresHpiroi2) == "Three_Letter_Country_Code"] <- "LOCATION"
DocNurcCont <- merge(DocNurc,XoresHpiroi2,by = "LOCATION")
DocNurcAm <- DocNurcCont[DocNurcCont$Continent_Name == "South America" | DocNurcCont$Continent_Name == "North America", ]
DocNurcEythAm <- ggplot(DocNurcAm, aes(x = Value.y, y = Value.x, color=LOCATION))
DocNurcEythAm + geom_point() + geom_smooth(method='lm')
GramGiatNos <- lm(giatroi ~ nosok)
summary(GramGiatNos)
if(!require(quantreg)){
    install.packages("quantreg")
    library(quantreg)
}
rq(giatroi ~ nosok)
rq(giatroi ~ nosok, tau = 0.15)
plot(giatroi ~ nosok) 
abline(rq(giatroi ~ nosok), col="red")
abline(rq(giatroi ~ nosok, tau = 0.15), col="blue")

Ευθείες παλινδρόμησης

Κώστας Κούδας

2025-08-25

1 Γραμμική παλινδρόμηση

1.1 Τυπικό σφάλμα εκτίμησης

2 Ποσοστημοριακή παλινδρόμηση