To promote safe driving habits and to better protect its customers, an insurance company offers a discount of between 5% and 20% on renewal insurance premiums to customers who have completed a defensive driving course. The following table of data shows the number of customers who have applied for the discount at various discount levels, over a period of 12 months.

Use the accompanying computer output to answer the following questions.
a. Determine the estimated equation of the straight-line regression of the number of customers applying for the discount (Y) on the discount level (X).
b. Determine the estimated equation of the quadratic regression of the number of customers applying for the discount (Y) on the discount level (X).
c. Plot both estimated models, along with a scatterplot of the data. Which model appears to fit the data better?
d. Conduct variables-added-in-order tests for the model in part (b).
e. Carry out tests for the significance of the straight-line regression in part (a) and for the adequacy of fit of the estimated regression line.
f. Carry out tests for the significance of the quadratic regression in part (b) and for the adequacy of fit of the second-order model.
g. Based on the results from parts (a) through (f), which of the two regressions appears to be more appropriate for predicting the number of customers who apply for the discount?

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Discount (X96) Number of Renewing Customers Applying for Discount Month 10 10 10 15 15 15 20 20 20 485 1,025 1,056 1,020 1.149 1,100 1,800 1,805 1,725 2.225 2,325 2,650 10 12 Straight-line regression of Y on X ANALYSIS OF VARIANCE Sum of Mean Sourco DF Squares SquareF Value Pr>F 90.18 .0001 1 42469564246956 10 470929 47093 11 4717885 Model Corrected Total 0.9002 0.8902 R-Square Root MSE Dopendent Mean Coeff Var 217.00893 530.41667 14.17973 Adj R-Sq PARAMETER ESTIMATES Parameter Standard Variabie e DF Estimate Error t Value Pr It Intercept 200.16667 153.44849 1.30 0.2213 1 106.42000 1120629 9.50 0001 Quadratic regression of Y on X ANALYSIS OF VARIANCE Sum of Mean DF Squares Square F Value Pr> F Source Model Error Corrected Total 54.90 0001 2 4360447 2180223 9 357438 39715 11 4717885 199.28707 1530 41667 13.02175 R-Square Adj R-Sq 0.9242 Root MSE Dependent Mean Coeff Var 0.9074 PARAMETER ESTIMATES Standard Error Variance tValue | Pr>It-Inflation Parameter Variable DF Estimate Intercept 1686.41667 320.30915 2.14 0.0607 9.17000 58.44244 0.6 0.8788 32.25000 X2 1 3.89000 2 30117 169 0.1252 32.25000 Portion of output omitted Type I Sum of DFI Squares R-Square F Value Pr>F Regression Linear Quadratic Total Model 0.9002 106.93 0001 2.86 0.1252 4360447 0.924254.90.0001 4246956 113491 0.0241 Sum of Residual Lack of Fit Pure Error Total Error DF SquaresMean Square F Value Pr>F 39990 8 317448 357438 39990 39681 39715 1.01 0.3448