Human capital theory suggests that those who have invested in higher levels of education will be able to command higher wages. A labour economist collected data on annual wages (Y, in $'000) and years of study (X) from a random sample of 12 employees to test this proposition. Assuming a linear relationship between Y and X, the labour economist used a least-squares method and found that the Y intercept = -23.50 and the slope = 9.73. Also, the sum of squares total (SST) and the sum of squares regression (SSR) were equal to 11132.92 and 8726.91, respectively. Based on this information, the standard error of the estimate is equal to __________. Round your final answer to two decimal places.
Question
Human capital theory suggests that those who have invested in higher levels of education will be able to command higher wages. A labour economist collected data on annual wages (Y, in $'000) and years of study (X) from a random sample of 12 employees to test this proposition. Assuming a linear relationship between Y and X, the labour economist used a least-squares method and found that the Y intercept = -23.50 and the slope = 9.73. Also, the sum of squares total (SST) and the sum of squares regression (SSR) were equal to 11132.92 and 8726.91, respectively. Based on this information, the standard error of the estimate is equal to __________. Round your final answer to two decimal places.
Solution
To find the standard error of the estimate, we first need to calculate the sum of squares error (SSE). This can be found by subtracting the sum of squares regression (SSR) from the sum of squares total (SST).
So, SSE = SST - SSR = 11132.92 - 8726.91 = 2406.01
The standard error of the estimate (Se) is then calculated by taking the square root of the SSE divided by the degrees of freedom. The degrees of freedom is calculated as n - 2, where n is the number of observations. In this case, n = 12.
So, degrees of freedom = 12 - 2 = 10
Therefore, Se = sqrt(SSE / degrees of freedom) = sqrt(2406.01 / 10) = sqrt(240.601)
Using a calculator, sqrt(240.601) = 15.51
So, the standard error of the estimate is 15.51, rounded to two decimal places.
Similar Questions
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