Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Problem set solutions for statistics 512, focusing on calculating confidence intervals using the bonferroni correction and constructing regression models with given data sets. Topics include anova, matrix operations, and multiple linear regression.

Typology: Assignments

Pre 2010

1 / 2

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