The following estimated regression model was developed relat

The following estimated regression model was developed relating yearly income(Y in $1,000s) of 30 individuals with their age(X_1) and and their gender(X_2) (0 if male and 1 if female) Y = 30 + 0.7X_1 + 3X_2 Also provided are SST = 2,000 and SSE = 500. Compute the coefficient of determination and fully interpret the meaning. 0.920, 92.0% of variation in dependent variable is explained by variation in the two independent variables. 0.875, 87.5% of variation in dependent variable is explained by variation in the two independent variables. 0.733,73.3% of variation in dependent variable is explained by variation in the two independent variables. 0.667, 66.7% of variation in dependent variable is explained by variation in the two independent variables. 0.750, 75.0% of variation in dependent variable is explained by variation in the two independent variables.

Solution

The coefficient of determination is calculated as

R² = 1 - ( SSE / SST ) = 1 - 500 / 2,000 = 0.75.

This means that 75.0% of the variation in the dependent variables is explained by the variation in the two independent variables. Hence, last option.