Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue t
ID: 3364677 • 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 Model Rating Price Year Make 18 19 18 19 16 19 18 17 17 15 14 16 17 16 13 ($1000) 1550.00 3900.00 1000.00 1200.00 310.00 2750.00 400.00 450.00 130.00 77.50 67.00 125.00 410.00 240.00 68.00 1984 Chevrolet Corvette 1956 1963 chevrolet Corvette couple (340-bhp 4-speed) 1978 Chevrolet Corvette couple Chevrolet Corvette 265/225-hp Silver Anniversary 1960-1963 Ferrari 1962-1964 Ferrari 1962 Ferrari 1967-1968 Ferrari 1968-1973 Ferrari 1962-1967 Jaguar 1969-1971 Jaguar 1971-1974 Jaguar 1951-1954 Jaguar 1950-1953 Jaguar 1956-1957 Jaguar 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 XKSSExplanation / Answer
a))) . Plot D is the correct scatter plot for the given data. Here the simple linear regression model is not appropriate to fit thid data. Since by observing the scatter plot we can see there are outliers and though the price and rate are positively related but we can not say it linear.
b))).
f=cbind(y,x,x2);f
y x x2 ;;;;Here y represents the price ;x represents rate and x2 represents squared rate)
[1,] 1550.0 18 324
[2,] 3900.0 19 361
[3,] 1000.0 18 324
[4,] 1200.0 19 361
[5,] 310.0 16 256
[6,] 2750.0 19 361
[7,] 400.0 18 324
[8,] 450.0 17 289
[9,] 130.0 17 289
[10,] 77.5 15 225
[11,] 67.0 14 196
[12,] 125.0 16 256
[13,] 410.0 17 289
[14,] 240.0 16 256
[15,] 68.0 13 169
> b=lm(y~x+x2);b
Call:
lm(formula = y ~ x + x2)
Coefficients:
(Intercept) x x2
33535.9 -4530.6 152.2
> summary(b)
Call:
lm(formula = y ~ x + x2)
Residuals:
Min 1Q Median 3Q Max
-1193.1 -291.1 119.4 258.1 1506.9
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 33535.92 13510.19 2.482 0.0288 *
x -4530.58 1670.00 -2.713 0.0189 *
x2 152.18 51.16 2.975 0.0116 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 661.1 on 12 degrees of freedom
Multiple R-squared: 0.703, Adjusted R-squared: 0.653
F-statistic: 14.17 on 2 and 12 DF, p-value: 0.0007
c)))
f2=cbind(y2,x3);f2
y2 x3 ;;;;; here y2 represents log(price) and x3 represents log(rate)
[1,] 7.35 2.89
[2,] 8.27 2.94
[3,] 6.91 2.89
[4,] 7.09 2.94
[5,] 5.74 2.77
[6,] 7.92 2.94
[7,] 5.99 2.89
[8,] 6.11 2.83
[9,] 4.87 2.83
[10,] 4.35 2.71
[11,] 4.20 2.64
[12,] 4.83 2.77
[13,] 6.02 2.83
[14,] 5.48 2.77
[15,] 4.22 2.56
> b1=lm(y2~x3);b1
Call:
lm(formula = y2 ~ x3)
Coefficients:
(Intercept) x3
-23.31 10.40
> summary(b1)
Call:
lm(formula = y2 ~ x3)
Residuals:
Min 1Q Median 3Q Max
-1.26004 -0.35803 -0.02004 0.41496 0.99573
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -23.308 4.395 -5.304 0.000143 ***
x3 10.402 1.561 6.664 1.55e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6569 on 13 degrees of freedom
Multiple R-squared: 0.774, Adjusted R-squared: 0.756
F-statistic: 44.41 on 1 and 13 DF, p-value: 1.554e-05
d))))))) By observing the R-squared and residuals we can conclude that the model in part(c) is preferable than model defined in part(b).
Note- o<R^2<1 and the value of R^2 closed to 1 is more preferable.