Question

Concern over the number of car thefts grew into a project to determine the relationship between car thefts in provinces and the variables, X1 = Police per 10,000 persons. X2 = Expenditure by local government for police protection, in thousands, and X3 = New passenger car registrations, in thousands. Data from 10 provinces were collected. The Excel/XLSTAT® regression results are

Regression equation: y= -25.3 + 1.28X1 + 0.0188X2 + 0.0969X3

Predictor	Coef	Stdev	t-ratio	p
Constant	-25.29	17.85	-1.42	0.190
X1	1.2831	0.9275	1.38	0.2
X2	0.018827	0.00846	2.23	0.053
X3	0.09686	0.03536	2.74	0.023

correlation between the variables

	car theft	X1	X2	X3
Car theft	1
X1	0.466	1
X2	0.970	0.390	1
X3	0.976	0.406	0.958	1

a. perform a test and see if the model is significant overall. alpla = 0.01

b. perform a test for each regression coef, using both 0.05 and 0.01 significance levels.

c. do the coefficients have the sign you might expect?

d. is there multicollinearity in this model?

Answer 1

a) overall model significance is measured using F test

Ho: all beta are equal to zero

Ha: Atleast one beta is not equal and non zero

F = R-squared / (1-p) /(1-R-sqaured) /(n-p)

where p is number of parametrs p=4

n is the number of observations n=10

R -squared is not given

model is significant if F > F critical value

b) lets look at the pvalue of the variables

X1 is not significant both at 5% and 1% as pvalaue is greater

X2 as well not significant on 5% and 1%

X3 is significant at 5% but not significant at 1%

c) no

X1 and X2 seems to be having negative sign but are positive. as with increases in polic facility the theft must decrease

X3 is positive and it is good and intuitive

d) As no correlations amongst two different independent variables is 1. so there is not multicollinearity in the model

d)