Assume that you get a coefficient of determination of 0.741, based on a sample size of 23, as shown in Figure 13.5. Further assume that the regression was based on 10 predictor variables. Given that there are 10 predictors as opposed to just 2, what R² would you expect to get by pure chance even when there is no relationship between the dependent and the independent variables?

Data from Figure 13.5

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A 1 Summary Output 2 Regression Statistics 3 Multiple R 4 R Square 5 Adjusted R Square 6 Standard Error 7 Observations 8 9 ANOVA 10 11 Regression 12 Residual 13 Total 14 15 16 Intercept 17 Square Feet 18 Age B C 57.35 0.017718 -0.6663 0.861 0.741 0.715 11.9604 23 Analysis of variance (ANOVA) table df 2 20 22 D SS 8189.7 2861.0 11050.7 Coefficient of determination Adjusted R² Standard error of the estimate (se) Coefficients Standard Error 10.01 0.003146 0.228 E MS 4094.9 143.1 F F Significance F 0.000 28.63 F test for the overall model t Stat P-value 5.73 0.000 0.000 5.63 -2.92 0.008 t test of regression coefficients and p-values