Exam - 5 Problems on Applied Regression Analysis | STAT 51200, Exams of Statistics

Download Exam - 5 Problems on Applied Regression Analysis | STAT 51200 and more Exams Statistics in PDF only on Docsity! Statistics 512 Midterm Exam 2 Tuesday, November 26, 2002 Time: 75 minutes Instructor: Dr. K. L. Simonsen Name: . You may detach the “Output” pages from the back of the exam. It is not necessary to hand those in unless you have done work on those pages and wish it to be considered. This exam is open-book and open-notes. Calculators are permitted. Please - do not cheat on this exam (i.e. do not communicate with any other person) - circle your answers where appropriate - write your solution clearly and legibly so that I can follow it - cross out your mistakes; do not erase large quantities of work - use the back of a page if you run out of room and indicate this on the question page - move on if you get stuck - do not feel that questions must be done in order - do not leave the room until the end of the class period Question Possible Actual 1 12 2 11 3 12 4 20 5 20 Total 75 (12) 1. A publisher wants to compare four different textbooks on regression. Their goal is to decide which books are more likely to be used in courses. In addition, they would like to know if there is much agreement among professors about texts. They randomly select fifteen statistics professors who agree to help. Each professor examines every book and assigns it a rating representing how much they would like to use it in their course. a) Identify by name the response variable and all factors in this experiment. (3) b) For each factor, state whether it should be considered a fixed or random effect. Justify your answers briefly. (4) c) State the following: (5) (i) the number of levels for each factor, (ii) the total number of treatments, (iii) the total sample size nT, and (iv) n, the number of observations per treatment. 4. Refer to the SAS output marked OUTPUT FOR PROBLEM 4. Greenhouse benches were set up as blocks. Within each block, plants of different genetic varieties were grown. The maximum height of each plant was measured. (20) a) Write the cell means model for this analysis. Include numerical values for the number of levels being compared and the numbers of observations per treatment. (3 pts) Also state the distributional assumption (2 pts). (5) b) Explain why no interaction term was included in the model (2 pts). Based on the graph shown, do you consider the assumption of no interaction to be justified? Give a yes or no answer (1 pt) and a detailed explanation of your answer (3 pts). Can you think of any way to improve this model (1 pt)? (7) (8) c) Write the factor effects model used for this analysis (3 pts). Then, give a numerical estimate for each parameter in the model (5 pts). (20)5. Refer to the SAS output marked OUTPUT FOR PROBLEM 5. a) Write the factor effects model used for this analysis (3 pts). Include numerical values for the number of levels being compared and the numbers of observations per treatment. (3 pts) Also state the distributional assumption (2 pts). (8) b) Summarize the results of the hypotheses tests for main effects and interactions. (6) c) Explain the results of the Tukey procedures for the main effects. (5) d) Estimate the residual variance σ2. (1) OUTPUT FOR PROBLEM 4 The GLM Procedure Dependent Variable: height Sum of Source DF Squares Mean Square F Value Pr > F Model 8 196.5800000 24.5725000 57.95 <.0001 Error 15 6.3600000 0.4240000 Corrected Total 23 202.9400000 R-Square Coeff Var Root MSE height Mean 0.968661 3.807911 0.651153 17.10000 Source DF Type III SS Mean Square F Value Pr > F variety 3 172.9200000 57.6400000 135.94 <.0001 bench 5 23.6600000 4.7320000 11.16 0.0001 Level of ------------height----------- variety N Mean Std Dev 1 6 18.0000000 1.83084680 2 6 21.0000000 0.96540147 3 6 15.5000000 0.76681158 4 6 13.9000000 1.06395489 Level of ------------height----------- bench N Mean Std Dev 1 4 18.2000000 3.25269119 2 4 16.4000000 2.57811301 3 4 16.3000000 3.10590835 4 4 17.1500000 3.40734501 5 4 18.6000000 3.10805405 6 4 15.9500000 3.40832315 var i et y 1 2 3 4 hei ght 12 13 14 15 16 17 18 19 20 21 22 23 bench 1 2 3 4 5 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 34 4 4 4 4 4 6