Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue t
ID: 2907717 • Letter: C
Question
Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue to increase in value. The following data show the rarity rating (1-20) and the high price ($1000) for 15 classic cars. Year Make Model Rating Price ($1000) Corvette 18 1700.00 4000.00 1963 Cht Corvette couple (340-bhp 4-speed) 18 1050.00 1978 Chevrolet Corvette couple Silver Anniversary 19 1250.00 370.00 2500.00 400.00 400.00 150.00 72.50 57,00 115.00 400.00 260.00 74.00 1984 Chevrolet 1956 Chevrolet Corvette 2 65/225-hp 19 250 GTE 2+2 250 GTL Lusso 250 GTO 275 GTB/4 NART Spyder 365 GTB/4 Daytona E-type OTS E-type Series II OTS E-type Series III OTS XK 120 roadster (steel) xK C-type XKSS 16 19 18 17 17 15 14 16 17 16 13 1960-1963 Ferrari 1962-1964 Ferrari 1962 Ferrari 1967-196B Ferrari 1968-1973 Ferrari 1962-1967 Jaguar 1969-1971 Jaguar 1971-1974 Jaguar 1951-1954 Jaguar 1950-1953 Jaguar 1956-1957 Jaguar a. Choose the correct scatter diagram of the data using the rarity rating as the independent variable and price as the dependent variable. Does a simple linear regression model appear to be appropriate? A. Price (S) 2500 2000 1500 100DExplanation / Answer
b.
The correct scatter diagram does not show a linear relation between rating and price. Thus,
A simple linear regression model does not appear to be appropriate.
b.
I have used R studio to perform the calculations.
Stored the Rating and Price data in vectors Rating and Price .
Running the below command in R, we get the multiple regression model.
model = lm(Price ~ Rating + I(Rating^2))
Price = 3266 - 4421 Rating + 149 Rating2
Using the command summary(model), we get the coefficient of determination as,
R2 = 0.692
Using the command anova(model), we get,
The value of F statistic for Rating2 is 8.17
p-value is 0.0144
c.
Running the below command in R, we get the multiple regression model.
model2 = lm(log(Price) ~ log(Rating))
log(Price) = -23.49 + 10.46 log(Rating)
Using the command summary(model2), we get the coefficient of determination as,
R2 = 0.775
Using the command anova(model2), we get,
The value of F statistic for log(Rating)is 44.68
p-value is 0.0000
d.
As, the F statistic and R2 of the model in part (c) is greater than that of part (b).
The model in part (c) is preferred because it provides a better fit.