Question

# SUMMARY OUTPUT Regression Statistics Multiple R 0.870402 R Square 0.7576 Adjusted R Square 0.68488 Standard Error...

 SUMMARY OUTPUT Regression Statistics Multiple R 0.870402 R Square 0.7576 Adjusted R Square 0.68488 Standard Error 1816.52 Observations 27 ANOVA df SS MS F Significance F Regression 6 2.06E+08 34376848 10.41804 2.81E-05 Residual 20 65994862 3299743 Total 26 2.72E+08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -4695.4 12622.97 -0.37197 0.713825 -31026.5 21635.66 -31026.5 21635.66 AGE 161.7028 126.5655 1.277621 0.216015 -102.308 425.7137 -102.308 425.7137 MILAGE -0.03441 0.023186 -1.4842 0.153346 -0.08278 0.013953 -0.08278 0.013953 HP 46.33786 10.27696 4.508908 0.000214 24.9005 67.77522 24.9005 67.77522 AUTOMATIC -98.5413 1422.364 -0.06928 0.945455 -3065.54 2868.458 -3065.54 2868.458 WEIGHT 16.98936 10.20147 1.665385 0.111424 -4.29052 38.26925 -4.29052 38.26925 DOORS -2073.7 1346.151 -1.54047 0.139121 -4881.72 734.3233 -4881.72 734.3233

1.What is the R2 ?

2. Is the model linear?

3. Are all the independent variables good?

4. Which variable would you remove first?

5. A blank stepwise procedure puts the most significant variable in first, adds the next variable that will improve the model the most. A blank stepwise regression begins with all the independent variables and deletes the least helpful.

1. R-square is the % variation explained in the dependent variable. Here, R-square value = 75.76%

2. Yes, the model is linear as the degree of all the variables is 1.

3. We are looking for significance of the independent variables here or those who have a p-value < 0.05. Hence we can say that only the variable HP is significant at a significance level of 0.05. Rest of the variables are not significant.

4. We will remove the variable with the lowest t-statistic or the highest p-value (which is the least significant). Hence, in this case we will remove the variable AUTOMATIC with the lowest t-statistic having -0.06928

5. Here, we will go with all the independent variables but the AUTOMATIC variable which is the least helpful or the least significant.

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