The output below is from the regression analysis for forecasting mile per gallon

Question

The output below is from the regression analysis for forecasting mile per gallon (MPG) of a car based on its top speed (SP in mph), weight (WT in 100lbs; that is, i.e., WT = 1 means 100lbs).

Answer the followings:

1. The model is significant overall.  TrueFalse

2. The value in cell _____ should be used for testing the following null hypothesis: H0: sp = wt = 0 (Click to select)F12B5E17E19

3. Is (are) there any insignificant independent variable(s)? (Click to select)Yes, SPYes, WTYes, SP and WTNo

4. The accuracy (or performance) of this model can be assessed based on (Click to select)B5B5 and B6B5, B6, and B7B5, B6, B7, and B8

5. If the information of horse power is added to the current model, the R2 of the new model will be greater than that of the current model. (Click to select)TrueFalseUnknown

6. If the information of horse power is added to the current model, the adjusted R2 of the new model will be greater than that of the current model. (Click to select)TrueFalseUnknown

7. Regardless of your answer to the questions above, assume that both SP and WT are significant. What is MPG of a certain car whose top speed is 100 and weight is 2500lbs. (Click to select)28.5233.6737.2441.65

1 SUMMARY OUTPUT Regression Statistics [Multiple R 5 R Square 6 Adjusted R Square 7 Standard Error 8 Observations 4.18 82 10 ANOVA Significance F 192.05 4.58964E-31 MS 6724 3362.22 12 Regression 13 Residual 14 Total 8 79 81 1383 17.51 8107 Coefficients Standard Error t Stat P-value Lower 95% 75.65 0.10 1.00 Upper 95% 83.40 0.01 0.84 3.89 19.44 7.71 17 Intercept 18 SP 19 WT 20 707E-32 67.90 0.08 -12.83 5.1977E-21 0.19 1.15

Explanation / Answer

Answers:

Question 1

Answer:

True

(Model is significant overall because p-value = 0.00 approximately is less than 0.05 or 0.01 alpha level of significance.)

Question 2

Answer:

E17E19

(…because this cell represents the p-values for regression coefficients i’s…)

Question 3

Answer:

No

(because all p-values in the given regression output are approximately equal to 0 which are less than the 5% level of significance or alpha = 0.05 or 0.01.)

Question 4

Answer:

B5, B6, and B7

(Because these three cells represent the values for R square, adjusted R square, and standard error which describe the accuracy of the regression model)

Question 5

Answer:

True

(As the number of predictors increases, the value of R square also increases)

Question 6

Answer:

False

(Adjusted R square does not affected by the increasing number of predictors)

Question 7

Answer:

Predicted MPG = 75.65 – 0.10*100 – 1.00*25 = 40.65

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