When using the t-statistic in multiple regression to determine if a variable should be removed: A) R² will increase if the variable is removed. B) if |t| 1, the standard error will decrease. C) a large number of independent variables is convenient. D) if |t|

Question

When using the t-statistic in multiple regression to determine if a variable should be removed: A) R² will increase if the variable is removed. B) if |t| > 1, the standard error will decrease. C) a large number of independent variables is convenient. D) if |t| < 1, the standard error will increase.

Quizplus · Accepted Answer

The t-statistic in multiple regression is used to test the null hypothesis that a coefficient is equal to zero (i.e., the variable has no effect). If a variable that is not statistically significant (suggested by a low |t| value) is removed, the model's R-squared (R²) may increase because the model becomes more parsimonious, removing noise or irrelevant information.

When Using the T-Statistic in Multiple Regression to Determine If