Question

Shown here are the data for y and three predictors, x1, x2, and x3. A stepwise...

Shown here are the data for y and three predictors, x1, x2, and x3. A stepwise regression procedure has been done on these data; the results are also given. Comment on the outcome of the stepwise analysis in light of the data.

y x1 x2 x3
94 21 1 204
97 25 0 198
93 22 1 184
95 27 0 200
89 31 1 183
91 20 1 159
91 18 1 147
94 25 0 196
98 26 0 228
99 24 0 242
90 28 1 162
92 23 1 180
96 25 0 219


Step 1 2 3
Constant 74.57 82.8 89.05
X3 0.1 0.064 0.07
T-Value 5.97 2.95 4.92
P-Value 0.000 0.014 0.001
X2 -2.53 -2.9
T-Value -2.2 -3.83
P-Value 0.053 0.004
X1 -0.297
T-Value -3.8
P-Value 0.004
S 1.59 1.37 0.895
R-Sq 76.43 % 84.11 % 93.9 %

Homework Answers

Answer #1

We are given the outcome of the stepwise Regression analysis. It is obvious that it is a forward type of stepwise regression analysis. In forward type, we start from a single explanatory variable and keep adding the other explanatory variable and check the fitness of model in each step.

To check the fitness of models, we have many criteria but out of the given output, we have two determinants first the significance of the variable and secondly the R-square.

We got all the explanatory variables significant in each step that indicates X1, X2 and X3 are significant to add in the model. Moreover, the R-square (93.9%) value is maximum for model 3. The R-square shows that amount of variation on Y (dependent variable) that can be explained through all the covariates. Therefore, at last, we can conclude that the model 3 is the best model and it is worth to add the variables x1, x2 and x3.

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