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: TIME_i
= β₀
+ β₁HP_i
+ β₂HP_i
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="">