Q.3 an analyst is concerned with setting the rates of car insurance premiums for
ID: 3363792 • Letter: Q
Question
Q.3 an analyst is concerned with setting the rates of car insurance premiums for different counties in a particular state. The following model estimates various insurance rates based on a number of variables.
Y=Bo + b1x1+b2x2+b3x3+b4x4=e
Where
Y= insurance premiums for each county
X1= expenditures on road improvements
X2= number of DUI/DWI arrests in previous year
X3= number of uninsured motorists
X4 = number of car thefts/burglaries in previous year
e=error term
The following is the SPSS output for the Ordinary Least Squares (OLS) estimation
MODEL Sum of Squares df Mean
Square F Sig.
Regression 195.501
Residual 500.689
Total 696.190 399
Coefficients
Model B S.E. Beta t Sig.
Constant -.822 1.136
X1 .123 0.15 .589
X2 -.116 .034 -.166
X3 .115 .030 .264
X4 .196 .117 .072
Question: write the null and alternative hypothesis for the F-test of overall significance of the model and compute F, test whether a significant relationship is present.
Explanation / Answer
Null Hypothesis : H0 : The relationship is not significant.
Alternative Hypothesis : H1 : The relationship is significant.
We will fill up the rest of the table.
The degree of freedom would be given by,
dfregression = n -1 = 4 - 1 = 3
dfresidual = dftotal - dfregression = 399 - 3 = 396
The mean squares would be given by,
MSregression = SSregression/dfregression = 195.501/3 = 65.167
MSresidual = SSresidual / dfresidual = 500.689/396 = 1.264
The F-statistic would be given by,
F = MSregression / MSresidual = 65.167/1.264 = 51.54
The corresponding P-value is 0.000
Since the p-value is very low, we will reject the null hypothesis. Hence the relationship is significant.
MODEL Sum of Squares df Mean squares F Sig. Regression 195.501 Residual 500.689 Total 696.190 399Related Questions
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