The following table gives relevant information for ten branches of an insurance

Question

The following table gives relevant information for ten branches of an insurance company.

The following table gives relevant information for ten branches of an insurance company. Use this data to develop a regression equation that could be used to predict the annual operation cost of a branch based on the number of home insurance policies and number of car insurance policies it handles. Suppose that a branch has 500 home insurance policies and 825 car insurance policies. Forecast its estimated annual operating cost. Within what range do you expect the forecast for annual operation cost to be accurate 68% of the time.

Explanation / Answer

following information is genetated about regression analysis from the given data

(a)cost=-10084+167.33*home+54.11*car

(b)cost=-10084+167.33*500+54.11*825=118222

(c)

(1-alpha)*100% confidence interval for sample mean=mean± z(alpha/2)*sd/sqrt(n)

here alpha=0.32 and n=10

68% confidence interval for sample mean=mean±z(0.32/2)*sd/sqrt(n)

=128500±1*55361/sqrt(10)=128500±17507=(110993,146007)

Analysis of Variance Source DF Sum of Mean F Value Pr > F Squares Square Model 2 3.055E+10 1.53E+10 1063.05 <.0001 Error 7 100576824 14368118 Corrected Total 9 3.065E+10 Root MSE 3790.53 R-Square 0.9967 Dependent Mean 128500 Adj R-Sq 0.9958 Coeff Var 2.94983 Parameter Estimates Variable DF Parameter Standard t Value Pr > |t| Estimate Error Intercept 1 -10084 3504.181 -2.88 0.0237 home 1 167.32669 5.89545 28.38 <.0001 car 1 54.10529 3.65587 14.8 <.0001

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