Background Information:OBSMAKEMODELTIMESPEEDWEIGHTHP HPTIME1AudiTT Roadster8.91331335150 1508.92Mini Cooper S7.41341240168 1687.43VolvoC70 T5 Sport7.41501711220 2207.44SaabNine-Three7.91491680247 2477.95Mercedes-BenzSL3506.61551825268 2686.66JaguarXK86.71541703290 2906.77BugattiVeyron 16.42.425319501000 10002.48LotusExige4.9147875189 1894.99BMWM3 (E30)6.71441257220 2206.710BMW330i Sport5.91551510231 2315.911PorscheCayman S5.31711350291 2915.312NissanSkyline GT-R (R34)4.71651560276 2764.713Porsche911 RS4.71721270300 3004.714FordShelby GT51501584319 319515MitsubishiEvo VII RS Sprint4.41501260320 3204.416Aston MartinV8 Vantage5.21751630380 3805.217Mercedes-BenzSLK55 AMG4.81551540355 3554.818MaseratiQuattroporte Sport GT5.11711930394 3945.119SpykerC84.51871275400 4004.520Ferrari288GTO4.91891161400 4004.921MoslerMT9003.91901130435 4353.922LamborghiniCountach QV4.91801447455 4554.923ChryslerViper GTS-R41901290460 460424BentleyArnage T5.21792585500 5005.225Ferrari430 Scuderia3.51981350503 5033.526SaleenS73.32401247550 5503.327LamborghiniMurcielago42051650570 570428PaganiZonda F3.62141230602 6023.629McLarenF13.22401140627 6273.230Koenigsegg CCR3.22421180806 8063.2 The TIME output corresponding to HP can be found as follows: SUMMARY OUTPUT Regression Statistics Multiple R 0.797539769 R Square 0.636069683 Adjusted R Square 0.623072172 Standard Error 0.945077588 Observations 30 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7.630122482 0.40417 18.87848641 1.83E-17 6.802217 8.458028 HP -0.00643163 0.000919 -6.99555614 1.32E-07 -0.00831 -0.00455 The fitted regression equation is: TIMEi=7.6301-0.0064 x HPi + ei Estimate the regression TIMEi = β0 + β1HPi + β2WEIGHTi + ε Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.936870335 1.29084 3.049851421 0.004964 1.292704 6.581036 WEIGHT 0.000776715 0.000861 0.902190335 0.374652 -0.00099 0.00254 The fitted regression equation is: TIME= 3.9369-0.00078 x WEIGHTi - ei In an effort to determine whether going to class improved student academic performance, David Romer1 developed the following equation: ?? = ?(???? ,??? ) + ?? Where: Gi = the grade of the ith student in Romer’s class (A=4, B=3, etc). ATTi = the percent of class lectures that the ith student attended PSi = the percent of the problem sets that the ith student completed 1. What signs do you expect for the coefficients of the independent variables in this equation? Explain your reasoning.2. Romer then estimated the equation: ?? ̂ = 1.07 + 1.74???? + 0.60??? ? = 195, ? 2 = 0.33 Do the estimated results agree with your expectations?

Question

Background Information:OBSMAKEMODELTIMESPEEDWEIGHTHP HPTIME1AudiTT Roadster8.91331335150 1508.92Mini Cooper S7.41341240168 1687.43VolvoC70 T5 Sport7.41501711220 2207.44SaabNine-Three7.91491680247 2477.95Mercedes-BenzSL3506.61551825268 2686.66JaguarXK86.71541703290 2906.77BugattiVeyron 16.42.425319501000 10002.48LotusExige4.9147875189 1894.99BMWM3 (E30)6.71441257220 2206.710BMW330i Sport5.91551510231 2315.911PorscheCayman S5.31711350291 2915.312NissanSkyline GT-R (R34)4.71651560276 2764.713Porsche911 RS4.71721270300 3004.714FordShelby GT51501584319 319515MitsubishiEvo VII RS Sprint4.41501260320 3204.416Aston MartinV8 Vantage5.21751630380 3805.217Mercedes-BenzSLK55 AMG4.81551540355 3554.818MaseratiQuattroporte Sport GT5.11711930394 3945.119SpykerC84.51871275400 4004.520Ferrari288GTO4.91891161400 4004.921MoslerMT9003.91901130435 4353.922LamborghiniCountach QV4.91801447455 4554.923ChryslerViper GTS-R41901290460 460424BentleyArnage T5.21792585500 5005.225Ferrari430 Scuderia3.51981350503 5033.526SaleenS73.32401247550 5503.327LamborghiniMurcielago42051650570 570428PaganiZonda F3.62141230602 6023.629McLarenF13.22401140627 6273.230Koenigsegg CCR3.22421180806 8063.2 The TIME output corresponding to HP can be found as follows: SUMMARY OUTPUT     Regression Statistics Multiple R 0.797539769 R Square 0.636069683 Adjusted R Square 0.623072172 Standard Error 0.945077588 Observations 30  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%  Intercept 7.630122482 0.40417 18.87848641 1.83E-17 6.802217 8.458028 HP -0.00643163 0.000919 -6.99555614 1.32E-07 -0.00831 -0.00455 The fitted regression equation is: TIMEi=7.6301-0.0064 x HPi + ei  Estimate the regression TIMEi = β0 + β1HPi + β2WEIGHTi + ε   Coefficients Standard Error t Stat P-value Lower 95% Upper 95%  Intercept 3.936870335 1.29084 3.049851421 0.004964 1.292704 6.581036 WEIGHT 0.000776715 0.000861 0.902190335 0.374652 -0.00099 0.00254  The fitted regression equation is: TIME= 3.9369-0.00078 x WEIGHTi - ei In an effort to determine whether going to class improved student academic performance, David Romer1 developed the following equation: ?? = ?(???? ,??? ) + ??  Where: Gi = the grade of the ith student in Romer’s class (A=4, B=3, etc).  ATTi = the percent of class lectures that the ith student attended  PSi = the percent of the problem sets that the ith student completed  1. What signs do you expect for the coefficients of the independent variables in this equation? Explain your reasoning.2. Romer then estimated the equation:  ?? ̂ = 1.07 + 1.74???? + 0.60???  ? = 195, ? 2 = 0.33 Do the estimated results agree with your expectations?

Accepted Answer

Given information:
The data represents the values of the variables time, weight, Hp and etc.

OBS	MAKE	MODEL	TIME	SPEED	WEIGHT	HP	HP	TIME
1	Audi	TT Roadster	8.9	133	1335	150	150	8.9
2	Mini	Cooper S	7.4	134	1240	168	168	7.4
3	Volvo	C70 T5 Sport	7.4	150	1711	220	220	7.4
4	Saab	Nine-Three	7.9	149	1680	247	247	7.9
5	Mercedes-Benz	SL350	6.6	155	1825	268	268	6.6
6	Jaguar	XK8	6.7	154	1703	290	290	6.7
7	Bugatti	Veyron 16.4	2.4	253	1950	1000	1000	2.4
8	Lotus	Exige	4.9	147	875	189	189	4.9
9	BMW	M3 (E30)	6.7	144	1257	220	220	6.7
10	BMW	330i Sport	5.9	155	1510	231	231	5.9
11	Porsche	Cayman S	5.3	171	1350	291	291	5.3
12	Nissan	Skyline GT-R (R34)	4.7	165	1560	276	276	4.7
13	Porsche	911 RS	4.7	172	1270	300	300	4.7
14	Ford	Shelby GT	5	150	1584	319	319	5
15	Mitsubishi	Evo VII RS Sprint	4.4	150	1260	320	320	4.4
16	Aston Martin	V8 Vantage	5.2	175	1630	380	380	5.2
17	Mercedes-Benz	SLK55 AMG	4.8	155	1540	355	355	4.8
18	Maserati	Quattroporte Sport GT	5.1	171	1930	394	394	5.1
19	Spyker	C8	4.5	187	1275	400	400	4.5
20	Ferrari	288GTO	4.9	189	1161	400	400	4.9
21	Mosler	MT900	3.9	190	1130	435	435	3.9
22	Lamborghini	Countach QV	4.9	180	1447	455	455	4.9
23	Chrysler	Viper GTS-R	4	190	1290	460	460	4
24	Bentley	Arnage T	5.2	179	2585	500	500	5.2
25	Ferrari	430 Scuderia	3.5	198	1350	503	503	3.5
26	Saleen	S7	3.3	240	1247	550	550	3.3
27	Lamborghini	Murcielago	4	205	1650	570	570	4
28	Pagani	Zonda F	3.6	214	1230	602	602	3.6
29	McLaren	F1	3.2	240	1140	627	627	3.2
30	Koenigsegg	CCR	3.2	242	1180	806	806	3.2

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.797539769
R Square	0.636069683
Adjusted R Square	0.623072172
Standard Error	0.945077588
Observations	30

Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.630122482	0.40417	18.87848641	1.83E-17	6.802217	8.458028
HP	-0.00643163	0.000919	-6.99555614	1.32E-07	-0.00831	-0.00455