Question

If a regression model is fit with two predictors (x1) and (x2) and the t-test p-values for each is large but when two simple linear regressions are fit each with only one of the predictors, the t-test p-values are small, the variables (x1) and (x2) are: (choose 1 one of the options below)

a) highly coorelated

b) both significant

c) insignificant

d) plain weird

Answer 1

For solving the prob;em and understanding the concpet we have to understand the concept of p value. P value is probability value which is used to accept or reject the null hypothesis on the basis of prespecified values of level of significance .

For this first frame the null and alternative hypothesis, and according to which the testing with p value can be achieved.

Then the best linear unbiased estimator is given by

When we fit regression with single predictor we have less p value and when we fit regression model with two predictor we have higher p value. Higher p value indicates the higher chances of accepring of null hypothesis and lower p value indicates the lower chances of accepting of null hypothesis. Therefor higher p suggests that null hypothseis is true means there is no linear realtionship between the variables this is due to the fact that both the predictors are highly correlated.

It indicates that it is a case of multicollinearity.

Ans is that both the predictors is highly correlated