3e] Are all of the four X variables needed in this model? Justify your answer. The regression equation is ioqmpq = 1.?5 - 0.000049 displacement - 0.000829 horsepower - 0.00021'3 weight r 0.029? year Predictor Coef SE Coef T P Constant 1.7467 0.14 BB 11.?3 0.000 displacement: 0.0000492 0.0001900 0.26 0.796 horsepower 0.0003292 0.0003731 2.19 0.029 weight: 0.0002'i'255 0.00002069 13.1]" 0.000 year 0.029737 0.0018 60 15.99 0.000 S = 0.121823 RSq = 8T.3% RSqtadj] = 87.2% Analysis of Variance Source DE' SS 1-15 F P Regression 4 39.4666 9.3666 664.01! 0.000 Residual Erma: 387 5.7434 0-0140 Total 391 45.2100 Choose the best answer from the following: i) When testing the null hypothesis that all the Beta's : 0, the pvaiue is 0.000 which is less than .05, so this hypothesis is rejected. This means that all of displacement, horsepower, weight, and year impact logmpg. ii} The variables weight and year are needed in the model because their pvalues are = 0.000. The other two variabtes are not needed. ,_., - ' iii) The only variable that is needed in the model is displacement since it is the only variable with a pvalue greater than .05. iv) The pvalue for displacement (J96 ) is greater than .05, thus displacement is not needed in the model. All the other 3 variabies have pvalues that are less than .05, therefore they are needed in the model