Consider a regression in which b₂ = -1.5 and the standard error of this coefficient equals 0.3. To determine whether X₂ is a significant explanatory variable, you would compute an observed t-value of -5.0.

Question

Quizplus · Accepted Answer

To determine if X₂ is a significant explanatory variable, we need to check if its coefficient is significantly different from zero. We can use the observed t-value, which is computed by dividing the coefficient estimate by its standard error (in this case, -1.5/0.3 = -5.0). If the observed t-value is larger than the critical t-value, which depends on the sample size and the significance level, we can reject the null hypothesis that the coefficient equals zero and conclude that X₂ is a significant explanatory variable. Since the observed t-value in this case is -5.0, which is larger than the critical t-value at any reasonable significance level, we can conclude that X₂ is indeed a significant explanatory variable.

Consider a Regression in Which B₂ = -1