1) (35pt) The CEO of a well-known car reseller company wants to determine the fa
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Question
1) (35pt) The CEO of a well-known car reseller company wants to determine the factors driving the resale value of a vehicle. The CEO knows that the resale value is an important factor considered by customers when buying a car. Assume you are performing a regression analysis using the data provided in the table below showing resale value, suggested price and type of vehicle (sport utility, small pickup). Suggested Resale Price? Type of Vehicle Value Vehicle Chevrclet Bazer LS Ford Explore Sport GMC Yuson XL 1500 9,495 20,495 26,789 18,965 6 30,186 25,745 Sport Ubity Sport Uity Sport Unity Sport Ulity Sport Usity Sport Ublty Sport Usity Sport Usity Sport Usity Sport Ublity Cvescole S-10 Extendec Cab Smalil Pckup Oodge Dakota Club Cab Sport Smail Pckup Ford Rançer XLT Reguiar Cab Small Pckup 57 - Honda CR-V 62 .lsuzu VebiCass Jeep Cherokee Limted Mercury Mounta ree Nissan Pathfincer XE Toyota 4Runner Toyota RAV4 .:ywocmaonSr23855% 26,919 22,418 7,148 18,847 6.870 53 18.51048 54 000015000 20000 2500030000 Ford Rançer XLT Suparcab Smail Pckup 20,225 55 44 Suggested Hetai Price ( GMC Sonoma Reguar Cao Small Pkup16.938 isuzu Homare Spacecab Small Pckup Mazca 84000 SE Cab Pus Small Pokup Nssan Fronber XE Ragula Smal Pckup Smail Pckup Smal Pckup 16,820 23.050 12,110 51 18.228 49 Toyota Tacoma šracan Toyota Tacoma Xiracabve 50Explanation / Answer
a.
R-squared the proportion of variation in the outcome Y, explained by the covariates X, is commonly described as a measure of goodness of fit. R-squared for Model 2 is 0.631. As R-squared lies between 0.5 and 0.75, model 2 with the explanatory variables suggested price and sport has moderate goodness of fit.
b.
The estimated regression equation for Model 2 is,
Resale value (%) = 42.554 + 0.000 * Suggested Price + 7.917 * Sport
c.
The p-value for intercept and Sport is less than the significance level of 0.05. So, the coefficients of Sport and intercept is statistically significant.
The p-value for suggested price (0.069) is greater than the significance level of 0.05. So, the coefficients of suggested price is not statistically significant.
d.
For suggested price as 0, the resale price for non-sport utility cars is estimated to be 42.554 %.
e.
For each one dollar increase is suggested price, the increase in resale price % is 0.
For sports vehicle, the increase in resale price % is 7.917 as compared with non-sports vehicle.
f.
The p-value for Sport is less than the significance level of 0.05. So, the coefficients of Sport is statistically significant and the variable Sport is an important explanatory variable in this model.
g.
R-square for Model 2 is larger than the quadratic model. Hence the best model which fits the data is Model 2.
h.
The regression equation is,
Resale price (%) = 56.72 - 0.0009 * Suggested Price + 0.0003 * Suggested Price2
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