Given below is the Microsoft® Excel output from regressing the monthly income ($) of 40-year-old South African men on number of years spent on education and number of years of job experience, using a data set of 2,000 randomly chosen 40-year-old South African men in the labour market. State the estimated multiple regression equation.

Question

BlackTom AI · Accepted Answer

To interpret the regression output, we need to examine the statistics that quantify how much of the variation in the dependent variable (monthly income) is explained by the model.
Option 1: 'Approximately 13.7% of the variation in the monthly income is explained by the regression model.' This matches the R-squared value shown as 0.13665 in the summary output, which indicates that about 13.7% of the variance in income is explained by the predictors (years of education and years of job experience). The approximation aligns with common rounding.
Option 2: 'Approximately 36.97% of the variation in the monthly income is explained by the regression model.' Here, 36.97% would correspond to R-squared near 0.3697. However, the printed R-squared value in the table is 0.13665, not 0.3697, so this statement overstates the variance explained by the model and conflates the concept with the reported Multiple R value.
Option 3: 'Approximately 36.97% of the monthly income is explained by the regression model.' This also misreads the statistics. Percent variation explained is tied to R-squared, not the raw scatter of income values. The correct R-squared value is substantially lower (around 13.7%), so this option is not consistent with the output.
Option 4: 'Approximately 13.7% of the monthly income is explained by the regression model.' Like Option 1, this uses the same correct interpretation as the 13.7% figure derived from R-squared. The wording duplicates Option 1, which is acceptable if it reflects the same numerical interpretation, though redundancy may be present.
Collectively, the key point is distinguishing between the multiple R and the R-squared statistic: Multiple R (the correlation between observed and predicted values) would be about 0.36967 (roughly 36.97%), whereas R-squared (the proportion of variance explained) is about 0.13665 (roughly 13.7%). The regression model’s explanatory power, as captured by R-squared, is the 13.7% figure, not 36.97%.
Thus, the options that align with the output’s R-squared interpretation are those stating approximately 13.7% of the variation in monthly income is explained by the regression model, whereas the 36.97% figures reflect a different statistic (Multiple R) and do not represent the variance explained by the model.

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