Let Z be a categorical variable with four levels: 1, 2, 3 and 4, and let X and Y be continuous. Using the following R output, estimate the average predicted value of Y in each category of Z when X is 10. ## ## ## Call: ## lm(formula = y - x * as. factor(z), data = d) ## ## Residuals: Min 1Q Median 3Q Max ## -4.0381 -1.7994 0.0844 1.8140 4.7927 ## ## Coefficients: Estimate Std. Error t value Pr>It!) ## (Intercept) 17.5027 40.2549 0.435 0.668 ## x 0.3116 10.4209 0.030 0.976 ## as. factor (z)1 27.2830 40.5103 0.673 0.507 ## as. factor(z)2 21.8574 40.3848 0.541 0.593 ## as. factor(z)4 10.2564 40.3781 0.254 0.802 ## x:as. factor (z)1 7.4968 10.5713 0.709 0.485 ## x:as. factor (z)2 5.6127 10.4778 0.536 0.597 ## x:as. factor(z)4 2.7892 10.4522 0.267 0.792 ## ## Residual standard error: 2.705 on 24 degrees of freedom ## Multiple R-squared: 0.844, Adjusted R-squared: 0.7985 ## F-statistic: 18.55 on 7 and 24 DF, p-value: 2.963e-08