Q.3 An analyst is concerned with setting the rates of car insurance premiums for
ID: 3363883 • 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
Questions:
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.
Interpet in words the understanding slope coefficients specifically in terms of the model. What did the standardized coeficients tell you, explain.
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
Questions:
Interpet in words the understanding slope coefficients specifically in terms of the model. What did the standardized coeficients tell you, explain.
Explanation / Answer
Result:
Model
B
S.E.
Beta
t
Sig.
Constant
-.822
1.136
X1
0.123
0.15
0.589
X2
-0.116
0.034
-0.166
X3
0.115
0.03
0.264
X4
0.196
0.117
0.072
Questions:
Interpet in words the understanding slope coefficients specifically in terms of the model. What did the standardized coeficients tell you, explain.
When X1 increases by 1 unit, y increases by 0.123 unit.
When X2 increases by 1 unit, y decreases by 0.116 unit.
When X3 increases by 1 unit, y increases by 0.115 unit.
When X4 increases by 1 unit, y increases by 0.196 unit.
Standardized coefficients tell how increases in the independent variables affect relative position within the group. We can determine whether a 1 standard deviation change in one independent variable produces more of a change in relative position than a 1 standard deviation change in another independent variable.
Using standardized regression coefficients is that we can compare the relative strength of the coefficients. Generally, the closer to the absolute value of 1 the coefficient is, the stronger the effect of that independent variable on the dependent variable (controlling for other variables in the equation). The closer the coefficient is to 0, the weaker the effect of that independent variable.
Model
B
S.E.
Beta
t
Sig.
Constant
-.822
1.136
X1
0.123
0.15
0.589
X2
-0.116
0.034
-0.166
X3
0.115
0.03
0.264
X4
0.196
0.117
0.072
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.