Regression Analysis

Cedric Alikusumah

ECON 217

March 15, 2017

Regression Analysis Assignment

X1	X2	X3	X4	X5	X6
	78	284	9.100000381	109
9.300000191	68	433	8.699999809	144
7.5	70	739	7.199999809	113
8.899999619	96	1792	8.899999619	97
10.19999981	74	477	8.300000191	206
8.300000191	111	362	10.89999962	124
8.800000191	77	671	10	152
8.800000191	168	636	9.100000381	162
10.69999981	82	329	8.699999809	150
11.69999981	89	634	7.599999905	134
8.5	149	631	10.80000019	292
8.300000191	60	257	9.5	108
8.199999809	96	284	8.800000191	111
7.900000095	83	603	9.5	182
10.30000019	130	686	8.699999809	129
7.400000095	145	345	11.19999981	158
9.600000381	112	1357	9.699999809	186
9.300000191	131	544	9.600000381	177
10.60000038	80	205	9.100000381	127
9.699999809	130	1264	9.199999809	179
11.60000038	140	688	8.300000191	80
8.100000381	154	354	8.399999619	103
9.800000191	118	1632	9.399999619	101
7.400000095	94	348	9.800000191	117
9.399999619	119	370	10.39999962	88
11.19999981	153	648	9.899999619	78
9.100000381	116	366	9.199999809	102
10.5	97	540	10.30000019	95
11.89999962	176	680	8.899999619	80
8.399999619	75	345	9.600000381	92
	134	525	10.30000019	126
9.800000191	161	870	10.39999962	108
9.800000191	111	669	9.699999809	77
10.80000019	114	452	9.600000381	60
10.10000038	142	430	10.69999981	71
10.89999962	238	822	10.30000019	86
9.199999809	78	190	10.69999981	93
8.300000191	196	867	9.600000381	106
7.300000191	125	969	10.5	162
9.399999619	82	499	7.699999809	95
9.399999619	125	925	10.19999981	91
9.800000191	129	353	9.899999619	52
3.599999905	84	288	8.399999619	110
8.399999619	183	718	10.39999962	69
10.80000019	119	540	9.199999809	57
10.10000038	180	668	13	106
	82	347	8.800000191	40
10	71	345	9.199999809	50
11.30000019	118	463	7.800000191	35
11.30000019	121	728	8.199999809	86
12.80000019	68	383	7.400000095	57
10	112	316	10.39999962	57
6.699999809	109	388	8.899999619	94

The data (X1, X2, X3, X4, X5) are by city.
X1 = death rate per 1000 residents
X2 = doctor availability per 100,000 residents
X3 = hospital availability per 100,000 residents
X4 = annual per capita income in thousands of dollars
X5 = population density people per square mile
Reference: Life In America's Small Cities, by G.S. Thomas

X6=gender where 0-male and 1-female

Briefly we are going to look at the relationship between X1 (death rate per 1000 residents) with X2 (doctor availability per 100,000 residents), X3 (hospital availability per 100,000 residents), X4 (annual per capita income in thousands of dollars), X5 (population density people per square mile) and X6 (gender).
Choosing death rate per 1000 residents as the response variables because the other variables (X1, X2, X3, X4, X5 and X6) explain the dependent variable.
The general model is: X1= a+bX2+cX3+dX4+eX5+fX6, where a, b, c, d, e and f are constants that need to be determined.
I think the relationship is that the death rate per 1000 residents increases with: decrease in doctor and hospital availability per 100000 residents and decreases in population density per square mile and decreases annual per capita income in thousands of dollars.
The estimated model is: X1= 12.4472698+0.006859042*X2 + 0.00695302* X3 + -0.336405998*X4 + -0.009687813 *X5 +-0.23263965 *X6.
The coefficient of determination is 0.148132225 which indicates the total variability in the multiple regression model. It measures the linear association between X1 and the rest of the independent variables. 14.81% of the total variation can be explained by the linear relationship between X1 and the independent variables. If X6(the dummy variable) is not considered the coefficient of determination remains 0.148132225.
The adjusted R square is 0.057507994
Using the F-test to check the validity of the model shows the model is statistically acceptable and valid.
The intercept is 12.4472698 is the point where the line of best fit and the y-axis intercept.
X2 coefficient is 0.006859042 which means that for each one unit increase in X2 per 100000 residents the death rate per 1000 residents increases by 0.006859042. This also applies to X3 coefficient which is positive and for each increase in X3 per 100000 residents the death rate per 1000 residents increases by 0.000695302.
X4, X5, X6 have negative coefficient that means for each one unit decrease in either X4,X5,X6 the death rate per 1000 residents decreases by the proportional coefficient.
P-value is used to check if individual variables are significant (if p-value is greater than 0.05 then the variable is not significant). Hence X5 and X6 are not significant as their individual p-values are greater than 0.05.