Final answer:
To determine the standard error of the slope coefficient given the slope and the t-statistic, use the formula SE = (slope estimate) / t. By inserting the provided values, SE = 1.93 / 24.125.
Step-by-step explanation:
The question asks about determining the standard error of the slope coefficient in a regression line equation. Given that the regression equation is earnings^ = -7.29 + 1.93 x years education and the t-statistic for the slope coefficient is 24.125, we can calculate the standard error by knowing that the t-statistic (t) is equal to the estimate of the parameter (in this case, the slope) divided by its standard error (SE). The formula would be t = (slope estimate) / (SE). To find the SE, we rearrange this formula to SE = (slope estimate) / t.
By placing the numbers into the formula, SE = 1.93 / 24.125, we can find the standard error of the slope coefficient. Remember that to find this on a calculator or using technology, we might use the LinRegTTest or similar statistical software. However, since we have the t-statistic and slope from the equation, we can do the calculation manually as well.