Question

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$ % 0 8 Format Painter B9#- Clipboard Font Formatting as a Alignment Number Tables F G H I Rating Par AB C Year Make Model 1984 Chevrolet Corvette 1956 Chevrolet Corvette 265/225 hp 1963 Chevrolet Corvette coupe (340-bhp 4-speed) 1978 Chevrolet Corvette coupe Silver Anniversary 1960-1963 Ferrari 250 GTE 2+2 7 1962-1964 Ferrari 250 GTL Lusso 1962 Ferrari 250 GTO 1967-1968 Ferrari 275 GTB/4 NART Spyder 10 1968-1973 Ferrari 365 GTB/4 Daytona 11 1962-1967 Jaguar E-type OTS 12 1969-1971 Jaguar E-type Series II OTS 13 1971-1974 Jaguar E-type Series III OTS 14 1951-1954 Jaguar XK 120 roadster (steel) 15 1950-1953 Jaguar XK C-type 16 1956-1957 Jaguar XKSS Price ($1000) 1600.0 4000.0 1000.0 1400.0 380.0 2550.0 425.0 420.0 120.0 77.5 66.0 140.0 440.0 230.0 66.0 Rating Rating? log(Rating) Price ($1000) 1600.0 4000.0 1000.0 1400.0 380.0 2550.0 log(Price) Formula #N/A #N/A #N/A #N/A #N/A #N/A Part b #N/A #N/A #NA #N/A #N/A #NA #N/A #N/A #N/A #N/A #N/A #N/A Data Saved to Cengage

Answer 1

a)

price 4500 4000 3500 3000 2500 2000 1500 1000 500 1 2 4 6 8 10 12 14 16 18 20

linear model is not appropriate

b)

price	rating	rating^2
1600	18	324
4000	19	361
1000	18	324
1400	19	361
380	16	256
2550	19	361
425	18	324
420	17	289
120	17	289
77.5	15	225
66	14	196
140	16	256
440	17	289
230	16	256
66	13	169

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8454
R Square	0.7147
Adjusted R Square	0.6671
Standard Error	648.7156
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	12650206.6792	6325103.3396	15.0300	0.0005
Residual	12	5049982.5542	420831.8795
Total	14	17700189.2333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	33664.9232	13256.3624	2.5395	0.0260	4781.7908
rating	-4550.7191	1638.6249	-2.7772	0.0167	-8120.9761
rating^2	152.9724	50.2008	3.0472	0.0101	43.5942

price = 33665 -4551 Rating + 153 Rating^2

R^2 = 0.715
F = 15.03
p-value = 0.0005

c)

log price)	log (Rating)
7.377759	2.890372
8.29405	2.944439
6.907755	2.890372
7.244228	2.944439
5.940171	2.772589
7.843849	2.944439
6.052089	2.890372
6.040255	2.833213
4.787492	2.833213
4.350278	2.70805
4.189655	2.639057
4.941642	2.772589
6.086775	2.833213
5.438079	2.772589
4.189655	2.564949

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8838
R Square	0.7811
Adjusted R Square	0.7642
Standard Error	0.6505
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	19.6233	19.6233	46.3776	0.0000
Residual	13	5.5006	0.4231
Total	14	25.1239
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-23.5333	4.3368	-5.4264	0.0001	-32.9024
log (Rating)	10.4817	1.5391	6.8101	0.0000	7.1566

log(price) = -23.533 + 10.482 log(Rating)

R^2 = 0.781
F = 46.38
p-value = 0.0000

Formulas

А rating 18 5. 6 price 2 1600 3 4000 4 1000 1400 380 7 2550 8 425 9 420 10 120 11 77.5 12 66 13 140 14 440 15 230 16 66 rating^2 =B2*B2 =B3*B3 =B4*B4 =B5*B5 =B6*B6 =B7*B7 =B8*B8 =B9*B9 =B10*B10 =B11*B11 =B12*B12 =B13*B13 =B14*B14 =B15*B15 =B16*B16 log price) =LN(A2) =LN(A3) =LN(A4) =LN(A5) =LN(A6) =LN(A7) =LN(AS) ELN(A9) =LN(A10) =LN(A11) ELN(A12) =LN(A13) =LN(A14) =LN(A15) ELN(A16) log (Rating) =LN(B2) =LN(B3) =LN(B4) =LN(B5) =LN(B6) =LN(B7) =LN(B8) =LN(B9) ELN(B10) =LN(B11) =LN(B12) ELN(B13) ELN(B14) =LN(B15) ELN(B16) 17 18 19

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