What is the value of the test statistic used to test the null hypothesis H0: \\b

Question

What is the value of the test statistic used to test the null hypothesis H0: eta_1=eta_2=01=2=0 vs. the alternative that at least one of the coefficients is not equal to 0? Round your answer to 1 decimal place.

2) An automobile using Regular gasoline will get, on average, how many more miles per gallon than an automobile with the same engine displacement that uses Premium gasoline? Round your answer to 2 decimal places.

3) What is the predicted MPG for an automobile with a 2.0 liter engine that uses Regular gasoline? Round your answer to 1 decimal place.

Explanation / Answer

1) TS =   332.6231568 = 332.6

2) the model is mpg ^ =b0 + b1*fuel + b2* displacement

fuel = 1 for premium else 0

hence required answer is b1

= -2.722958426

= -2.72

3) here displacement = 2 , fuel = 0 {Regular

hence

MPG^ =   40.59456529 - 3.194400513 *2

= 34.2057642

=34.21

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SUMMARY OUTPUT Regression Statistics Multiple R 0.827611557 R Square 0.684940889 Adjusted R Square 0.682881679 Standard Error 3.20679604 Observations 309 ANOVA df SS MS F Significance F Regression 2 6841.08764 3420.543818 332.6231568 1.79466E-77 Residual 306 3146.7635 10.28354084 Total 308 9987.85113 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 40.59456529 0.4906405 82.73790111 1.8206E-211 39.62910905 41.56002 39.62911 41.56002154 Fuel -2.722958426 0.42217481 -6.449836298 4.36512E-10 -3.553691535 -1.89223 -3.55369 -1.892225317 Displacement -3.194400513 0.1701453 -18.77454467 7.43392E-53 -3.529203369 -2.8596 -3.5292 -2.859597656

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