9. The following data were obtained from a sample of 12 respondents. Suppose tha
ID: 3311808 • Letter: 9
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9. The following data were obtained from a sample of 12 respondents. Suppose that we started by calculating a bivariate regression equation which predicted children's education using information on fathers' education. Suppose further that we then calculated a multiple regression equation which predicted children's education using information on both fathers' education and mothers' education. What would you expect to happen to the sum of squares regression in the multiple regression equation relative to the sum of squares regression in the bivariate linear regression equation? Does it increase or decrease in value? Why? Highest Grade of School Completed (Respondent 12 14 14 10 14 16 15 12 16 14 15 14 Highest Grade of School Highest Grade of School Completed (Father 12 10 14 Completed (Mother 12 12 12 12 12 12 12 10 6 16 13 14 14 6 20 13 12 14 Mean St. Dev. Variance 13.83 1.75 3.06 11.75 2.90 8.02 11.50 3.90 15.18Explanation / Answer
sum of square due to regression will increase.
we are using the least squares method. Any set of coefficients we choose must give a sum of squared residuals at least as great as for the best fit. Suppose we fit the model with the coefficients of the additional variables set to zero. This is the same as the fit without the additional variables, and as it restricts the coefficients, the sum of squares must be suboptimal except in the unlikely event that the least squares fit has these coefficinetns exactly zero.
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