Question

If you have two regressions with intercept, one with one explanatory variable (X), and another one with two explanatory variables (X and Z), the t statistic of the intercept will have the same value in both regressions.

True

False

Answer 1

False.

 

Explanation:

In the two regressions, the t statistic representing the intercept will be distinct from one another. In the case of the regression in which there is only one variable used for explanation, the t statistic will be equal to the coefficient divided by the standard error. The t statistic for the regression with two explanatory variables will be equal to the coefficient divided by the standard error multiplied by the square root of the variance inflation factor. This will be the case when the regression is performed with two variables.

 

Explain more:

The significance of the coefficient is evaluated using a statistic known as the t statistic. The significance of the coefficient is proportional to the size of the t statistic. In the context of the regression, the coefficient of the constant term is referred to as the intercept. When all of the variables that explain it are set to zero, the value that is represented by the intercept is the expected value of the response variable.

 

If there is just one variable that could explain the results of the regression, then the t statistic for the intercept will be equal to the coefficient divided by the standard error. The t statistic for the intercept in a regression with two explanatory variables will be equal to the coefficient divided by the standard error multiplied by the square root of the variance inflation factor. This will be the case when the regression involves two variables. A measure of the degree to which the data exhibit multicollinearity is referred to as the variance inflation factor. The phenomenon known as multicollinearity occurs when the variables that are supposed to explain something are highly connected with each other.

False