Statistics Problem Set 512: Analyzing Confidence Intervals and Regression - Prof. Kristofe, Assignments of Statistics

Download Statistics Problem Set 512: Analyzing Confidence Intervals and Regression - Prof. Kristofe and more Assignments Statistics in PDF only on Docsity! Statistics 512: Problem Set No. 4 Due October 3, 2008 1. Consider the following SAS output giving 5 confidence intervals for the mean of Y . If you wanted to guarantee that joint coverage of the five confidence intervals was at least 95%, what confidence level would you use when forming each interval, using the Bonferroni correction? Compute this adjusted confidence interval for the mean of Y when X = 5. (Note that some observations have been omitted from the output.) Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 16183 16183 805.62 <.0001 Error 16 321.39597 20.08725 Corrected Total 17 16504 Root MSE 4.48188 R-Square 0.9805 Dependent Mean 64.00000 Adj R-Sq 0.9793 Coeff Var 7.00294 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 -2.32215 2.56435 -0.91 0.3786 x 1 14.73826 0.51926 28.38 <.0001 Output Statistics Dep Var Predicted Std Error Obs x y Value Mean Predict 95% CL Mean Residual 3 5 78.0000 71.3691 1.0878 69.0630 73.6752 6.6309 4 1 10.0000 12.4161 2.1021 7.9598 16.8724 -2.4161 6 4 62.0000 56.6309 1.0878 54.3248 58.9370 5.3691 8 3 39.0000 41.8926 1.3125 39.1103 44.6750 -2.8926 10 2 33.0000 27.1544 1.6737 23.6064 30.7024 5.8456 2. Based on the following small data set, construct the design matrix, X, its transpose X′, and the matrices X′X, (X′X)−1, X′Y, and b = (X′X)−1X′Y. (Chapter 5 in the book discusses finding the inverse of a matrix.) X Y 2 1 4 2 6 3 8 7 10 9 1