# 1. Return to the ‘cars.xlsx’ dataset that was used in the Unit 6 Homework. Recall that this dataset includes data on the 0-60 time (TIME), top speed (SPEED), curb weight (WEIGHT), and horsepower (HP)...

1. Return to the ‘cars.xlsx’ dataset that was used in the Unit 6 Homework. Recall that this dataset includes data on the 0-60 time (TIME), top speed (SPEED), curb weight (WEIGHT), and horsepower (HP) of 30 automobiles.

There are good reasons based in physics to believe that the relationship between horsepower and 0-60 time is non-linear. Look again at the scatter plot of HP (x-axis) and 0-60 time (y-axis) from the Unit 6 Homework. To test the goodness of fit of one possible non-linear relationship estimate the following quadratic regression: TIMEi
= β0
+ β1HPi
+ β2HPi
2
+ ε Please include your regression results with your answers (and submit the excel file to the D2L dropbox for the Unit 7 Homework).

Compare the results from this regression to those from the Unit 6 Homework. Which do you prefer and why?

Sheet1 1.a. SUMMARY OUTPUTI expect a negative linear relationshp between HP and time. Regression Eqn: time = 7.63 - 0.00643*HP Regression StatisticsSlope = - 0.00643 Multiple R0.797539769With a unit increase in HP there is -0.00643 units decrease in time. R Square0.6360696831ho:coefficient of Hp is NOT significant Adjusted R Square0.6230721717h1:coefficient of Hp is significant Standard Error0.9450775883with t = -6.99 and p-value < 0.05, i reject ho and conclude that observations30coefficient of hp is significant anova1.b. dfssmsfsignificance f regression143.709860527143.709860527148.93780566440.0000001315 residual2825.00880613960.8931716478 total2968.7186666667 coefficientsstandard errort statp-valuelower 95%upper 95%lower 95.0%upper 95.0% intercept7.63012248240.404170245318.87848640871.83259006978913e-176.80221726548.45802769936.80221726548.4580276993 hp-0.00643163460.0009193886-6.99555613690.0000001315-0.0083149168-0.0045483524-0.0083149168-0.0045483524 yes, trend equation scatterplot confirms the above expected effect of increasing horsepower on 0-60 time scatterplot hp 8.97.47.47.96.66.72.44.90000000000000046.75.95.34.74.754.40000000000000045.24.85.09999999999999964.54.90000000000000043.94.900000000000000445.23.53.343.63.23.21501682202472682901000189220231291276300319320380355394400400435455460500503550570602627806hp time cars7 obsmakemodeltimespeedweighthp 1auditt roadster8.91331335150 2mini cooper s7.41341240168 3volvoc70 t5 sport7.41501711220 4saabnine-three7.91491680247 5mercedes-benzsl3506.61551825268 6jaguarxk86.71541703290 7bugattiveyron 16.42.425319501000 8lotusexige4.9147875189 9bmwm3 (e30)6.71441257220 10bmw330i sport5.91551510231 11porschecayman s5.31711350291 12nissanskyline gt-r (r34)4.71651560276 13porsche911 rs4.71721270300 14fordshelby gt51501584319 15mitsubishievo vii rs sprint4.41501260320 16aston martinv8 vantage5.21751630380 17mercedes-benzslk55 amg4.81551540355 18maseratiquattroporte sport gt5.11711930394 19spykerc84.51871275400 20ferrari288gto4.91891161400 21moslermt9003.91901130435 22lamborghinicountach qv4.91801447455 23chryslerviper gts-r41901290460 24bentleyarnage t5.21792585500 25ferrari430 scuderia3.51981350503 26saleens73.32401247550 27lamborghinimurcielago42051650570 28paganizonda f3.62141230602 29mclarenf13.22401140627 30koenigsegg ccr3.22421180806 http://www.strikeengine.com/performance-car-specs-0-60-0-100-power-weight-top-speed.html 0.05,="" i="" reject="" ho="" and="" conclude="" that="" observations="" 30="" coefficient="" of="" hp="" is="" significant="" anova="" 1.b.="" df="" ss="" ms="" f="" significance="" f="" regression="" 1="" 43.7098605271="" 43.7098605271="" 48.9378056644="" 0.0000001315="" residual="" 28="" 25.0088061396="" 0.8931716478="" total="" 29="" 68.7186666667="" coefficients="" standard="" error="" t="" stat="" p-value="" lower="" 95%="" upper="" 95%="" lower="" 95.0%="" upper="" 95.0%="" intercept="" 7.6301224824="" 0.4041702453="" 18.8784864087="" 1.83259006978913e-17="" 6.8022172654="" 8.4580276993="" 6.8022172654="" 8.4580276993="" hp="" -0.0064316346="" 0.0009193886="" -6.9955561369="" 0.0000001315="" -0.0083149168="" -0.0045483524="" -0.0083149168="" -0.0045483524="" yes,="" trend="" equation="" scatterplot="" confirms="" the="" above="" expected="" effect="" of="" increasing="" horsepower="" on="" 0-60="" time="" scatterplot="" hp="" 8.9="" 7.4="" 7.4="" 7.9="" 6.6="" 6.7="" 2.4="" 4.9000000000000004="" 6.7="" 5.9="" 5.3="" 4.7="" 4.7="" 5="" 4.4000000000000004="" 5.2="" 4.8="" 5.0999999999999996="" 4.5="" 4.9000000000000004="" 3.9="" 4.9000000000000004="" 4="" 5.2="" 3.5="" 3.3="" 4="" 3.6="" 3.2="" 3.2="" 150="" 168="" 220="" 247="" 268="" 290="" 1000="" 189="" 220="" 231="" 291="" 276="" 300="" 319="" 320="" 380="" 355="" 394="" 400="" 400="" 435="" 455="" 460="" 500="" 503="" 550="" 570="" 602="" 627="" 806="" hp="" time="" cars7="" obs="" make="" model="" time="" speed="" weight="" hp="" 1="" audi="" tt="" roadster="" 8.9="" 133="" 1335="" 150="" 2="" mini="" cooper="" s="" 7.4="" 134="" 1240="" 168="" 3="" volvo="" c70="" t5="" sport="" 7.4="" 150="" 1711="" 220="" 4="" saab="" nine-three="" 7.9="" 149="" 1680="" 247="" 5="" mercedes-benz="" sl350="" 6.6="" 155="" 1825="" 268="" 6="" jaguar="" xk8="" 6.7="" 154="" 1703="" 290="" 7="" bugatti="" veyron="" 16.4="" 2.4="" 253="" 1950="" 1000="" 8="" lotus="" exige="" 4.9="" 147="" 875="" 189="" 9="" bmw="" m3="" (e30)="" 6.7="" 144="" 1257="" 220="" 10="" bmw="" 330i="" sport="" 5.9="" 155="" 1510="" 231="" 11="" porsche="" cayman="" s="" 5.3="" 171="" 1350="" 291="" 12="" nissan="" skyline="" gt-r="" (r34)="" 4.7="" 165="" 1560="" 276="" 13="" porsche="" 911="" rs="" 4.7="" 172="" 1270="" 300="" 14="" ford="" shelby="" gt="" 5="" 150="" 1584="" 319="" 15="" mitsubishi="" evo="" vii="" rs="" sprint="" 4.4="" 150="" 1260="" 320="" 16="" aston="" martin="" v8="" vantage="" 5.2="" 175="" 1630="" 380="" 17="" mercedes-benz="" slk55="" amg="" 4.8="" 155="" 1540="" 355="" 18="" maserati="" quattroporte="" sport="" gt="" 5.1="" 171="" 1930="" 394="" 19="" spyker="" c8="" 4.5="" 187="" 1275="" 400="" 20="" ferrari="" 288gto="" 4.9="" 189="" 1161="" 400="" 21="" mosler="" mt900="" 3.9="" 190="" 1130="" 435="" 22="" lamborghini="" countach="" qv="" 4.9="" 180="" 1447="" 455="" 23="" chrysler="" viper="" gts-r="" 4="" 190="" 1290="" 460="" 24="" bentley="" arnage="" t="" 5.2="" 179="" 2585="" 500="" 25="" ferrari="" 430="" scuderia="" 3.5="" 198="" 1350="" 503="" 26="" saleen="" s7="" 3.3="" 240="" 1247="" 550="" 27="" lamborghini="" murcielago="" 4="" 205="" 1650="" 570="" 28="" pagani="" zonda="" f="" 3.6="" 214="" 1230="" 602="" 29="" mclaren="" f1="" 3.2="" 240="" 1140="" 627="" 30="" koenigsegg="" ccr="" 3.2="" 242="" 1180="" 806="">

## Answer To: 1. Return to the ‘cars.xlsx’ dataset that was used in the Unit 6 Homework. Recall that this dataset...

David answered on Nov 30 2019
CARS7
OBS    MAKE    MODEL    TIME    SPEED    WEIGHT    HP    HP^2
1    Audi    TT Roadster    8.9    133    1335    150    22500
2    Mini     Cooper S    7.4    134    1240    168    28224
3    V
olvo    C70 T5 Sport    7.4    150    1711    220    48400
4    Saab    Nine-Three    7.9    149    1680    247    61009
5    Mercedes-Benz    SL350    6.6    155    1825    268    71824
6    Jaguar    XK8    6.7    154    1703    290    84100
7    Bugatti    Veyron 16.4    2.4    253    1950    1000    1000000
8    Lotus    Exige    4.9    147    875    189    35721
9    BMW    M3 (E30)    6.7    144    1257    220    48400
10    BMW    330i Sport    5.9    155    1510    231    53361
11    Porsche    Cayman S    5.3    171    1350    291    84681
12    Nissan    Skyline GT-R (R34)    4.7    165    1560    276    76176
13    Porsche    911 RS    4.7    172    1270    300    90000
14    Ford    Shelby GT    5    150    1584    319    101761
15    Mitsubishi    Evo VII RS Sprint    4.4    150    1260    320    102400
16    Aston Martin    V8 Vantage    5.2    175    1630    380    144400
17    Mercedes-Benz    SLK55 AMG    4.8    155    1540    355    126025
18    Maserati    Quattroporte Sport GT    5.1    171    1930    394    155236
19    Spyker    C8    4.5    187    1275    400    160000
20    Fe
ari    288GTO    4.9    189    1161    400    160000
21    Mosler    MT900    3.9    190    1130    435    189225
22    Lamborghini    Countach QV    4.9    180    1447    455    207025
23    Chrysler    Viper GTS-R    4    190    1290    460    211600
24    Bentley    Arnage T    5.2    179    2585    500    250000
25    Fe
ari    430 Scuderia    3.5    198    1350    503    253009
26    Saleen    S7    3.3    240    1247    550    302500
27    Lamborghini    Murcielago    4    205    1650    570    324900
28    Pagani    Zonda F    3.6    214    1230    602    362404
29    McLaren    F1    3.2    240    1140    627    393129
30    Koenigsegg...
SOLUTION.PDF