Question

We run the following linear regression model in Excel (or any other softwares) Yi = β0 + β1Xi + β2Wi + εi , where i = 1, 2, . . . , 100. The results suggest that the slope on Xi is 97.28 with t-statistics 0.91, and the slope on Wi is 15.81 with t-statistics 11.39. What does it tell us?

Answer 1

The slope on Xi is 97.28 means that for 1 unit change in Xi, Yi with increase by 97.28 units if other factors are kept constant. And Xi with t-statistics 0.91 indicate the precision of the coefficient of Xi at a given level of significance. T-value is a measure of coefficient divided by its standard deviation. Here since the t-value is not larger than 2.5, it is considered to be significant.

The slope on Wi is 15.81 means that for 1 unit change in Wi, Yi with increase by 15.81 units if other factors are kept constant. And Wi with t-statistics 11.39 indicate the precision of the coefficient of Wi at a given level of significance. Here since the t-value is considerably larger than 2.5, it is considered to be insignificant.

Note: The critical t-values can be calculated from tables asa per corresponding dfs and level of significance.