Question

8. Calculating SSR, SSE, SST, and R-squared

Suppose you are interested in studying the effects of education on wages. You gather four data points and use ordinary least squares (OLS) to estimate the following simple linear model:

wage=β0+β1educ+u

where

	wage = hourly wage in dollars
	educ = years of formal education

After running your regression, you decide to examine how the fitted values of wages from your regression compare to the actual wages in your data set. These data are summarized in the following table:

obsno	wagei	wagei (hat)	residuals
			ui (hat) =wagei−wagei (hat)
1	17	18.5	-1.5
2	25	23.5	1.5
3	30	28.5	1.5
4	32	33.5	-1.5

Based on the data in the table, the explained sum of squares (SSE) is .

Based on the data in the table, the residual sum of squares (SSR) is     .

Based on the data in the table, the total sum of squares (SST) is   .

While you are skeptical of your OLS regression due to the low number of data points, you decide to calculate the R-squared of the regression to understand how well the independent variable educ explains the dependent variable wage. The resulting R2 is   .

Answer 1