Assume Multiple Linear Regression was performed and the following p-values were

Question

Assume Multiple Linear Regression was performed and the following p-values were calculated for each of the independent variables: Hours Studied (X1): p-value = 0.0002 Sleep (X2): p-value = 0.0101 Exercise (X3): p-value = 0.0769 Describe which variables should remain in the Regression Model and which variables should be removed based on an Alpha value of 0.05. Explain your reasoning behind your decision. NOTE: the hypothetical example mentioned earlier in our discussion is shared below for reference: y = 42 + 10X1 + 3.2X2 + 1.5X3 y represents final test score, X1 represents hours studied, X2 represents hours of sleep the night before the test, and X3 represents hours of exercise during the week of the test

Explanation / Answer

We consider any variable as non significant if the p - value corresponding to that variable is greater than alpha.

Here Alpha = 0.05

And we can see that for X1 and X2, p - values are less than 0.05 but for X3, p - value is greater than 0.05.

Hence,

We should remove X3 i.e. Hours of exercise during the week of the test because it is not a significant predictor for final test score.

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