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 error sum of squares (SSE) were equal to 11132.92 and 2406,01, respectively. Based on this information, we can say that a. around 21.61% of the variation in Y is explained by the variation in X. b. around 21.61% of the sample variability in Y is due to factors other than X c. around 78.39% of the sample variability in Y is due to factors other than X d. around 21.61% of the variation in X is explained by the variation in Y.
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 error sum of squares (SSE) were equal to 11132.92 and 2406,01, respectively. Based on this information, we can say that a. around 21.61% of the variation in Y is explained by the variation in X. b. around 21.61% of the sample variability in Y is due to factors other than X c. around 78.39% of the sample variability in Y is due to factors other than X d. around 21.61% of the variation in X is explained by the variation in Y.
Solution
The coefficient of determination (R^2) is a measure of the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It is calculated as 1 - (SSE/SST).
Given the values of SST = 11132.92 and SSE = 2406.01, we can calculate R^2 as follows:
R^2 = 1 - (SSE/SST) = 1 - (2406.01/11132.92) = 0.7839 or 78.39%
This means that 78.39% of the variation in Y is explained by the variation in X. Therefore, the remaining 21.61% of the variation in Y is due to factors other than X.
So, the correct answer is:
c. around 78.39% of the sample variability in Y is due to factors other than X.
Similar Questions
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. The labour economist also found that the standard error of the slope was 1.61. Based on this information, what statistical decision would you made if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? a. Accept the null hypothesis. b. Reject the null hypothesis. c. Do not reject the null hypothesis. d. Reject the alternative hypothesis.
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