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# 611 Review Sheet for STAT 51200 with Professor Jennings at Purdue

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Date Created: 02/06/15
Statistics 512 Review Problems for Second Midterm Exam Keep for Second Exam Review November 17 1 Short answer questions Each part is unrelated a The true means m7 2 M3 in a cell means model have values 407 507 and 407 respectively The error variance 02 is 207 and the design is balanced with 4 replicates per level What is the distribution of the following contrast estimate I Y1 Y2 7 2Y3 b In a 2 x 2 ANOVA7 the population means are lam 207 pg 257 M13 317 and M22 36 ls there an interaction in this model Explain why or why not c After performing a least squares regression7 you nd that the squares of the residuals are linearly related to the predictor X according to the following equation Em z 1 Xi You decide to use weighted linear regression in relating the response Y to the predictor X Give a formula for the weights w in terms of the variables in the model Assume all the Xi are positive d Given the following plot of M versus 01 what transformation of the response would you recommend to make the variance constant o co Group Standard Deviation 4 0 4 5 50 55 35 30 5 6 7 8 9 Group Mean e A two way additive ANOVA model has 3 and 4 levels for the two factors If the data have 25 observations ie7 nT 257 what is the error degrees of freedom f Show that the criterion Cp p is equivalent to the criterion MSEP lt 1 M SEFull g The price per unit increases with lot size until the size is 200 The price per unit stays constant for lot sizes greater than 200 In other words7 the function relating price to lot size is a piecewise linear function The slope of the line for lot size greater than 200 is zero The output from proc print after reading in the data is Obs cost lotsize cslope 1 1287 100 2 1077 125 3 850 150 4 703 175 5 483 200 6 460 225 7 476 250 8 479 275 9 483 300 Fill in an additional column of predictor values under the cslope heading that you would use to t the previously described piecewise linear model What model statement would you use in proc reg for this model 2 Refer to the SAS output marked OUTPUT FOR PROBLEM 2 a Write the factor effects model used for this analysis lnclude numerical values for the number of levels being compared and the numbers of observations per treatment Also state the distributional assumption b Summarize the results of the hypothesis tests for main effects and interactions c Explain the results of the Tukey procedures for the main effects d Estimate the residual variance 02 3 Refer to the SAS output marked OUTPUT FOR PROBLEM 3 Greenhouse benches were set up as blocks Within each block7 plants of different genetic varieties were grown The maximum height of each plant was measured a Write the cell means model for this analysis lnclude numerical values for the number of levels being compared and the numbers of observations per treatment Also state the distributional assumption b Explain why no interaction term was included in the model Describe graphical evidence that would justify this assumption of no interaction c Write the factor effects model used for this analysis Then7 give a numerical estimate for each parameter in the model Dependent Variable Y Source Model Error Corrected Total Source AB Source AB OUTPUT FOR PROBLEM 2 The GLM Procedure Sum of DF Squares Mean Square F Value 5 2040351465 408070293 1291 18 569141953 31618997 23 2609493418 RSquare Coeff Var Root MSE Y Mean 0781896 1856378 5623077 3029058 DF Type I SS Mean Square F Value 2 253610880 126805440 401 1 1749641113 1749641113 5534 2 37099471 18549736 059 DF Type III SS Mean Square F Value 2 253610880 126805440 401 1 1749641113 1749641113 5534 2 37099471 18549735 059 Tukey s Studentized Range HSD Test for Y Alpha 005 Error Degrees of Freedom 18 Error Mean Square 31619 Critical Value of Studentized Range 360930 Minimum Significant Difference 71755 Means with the same letter are not significantly different Tukey Grouping A A B A B B Mean 34619 29468 26785 N A Pr gt F lt0001 Pr gt F 00363 lt0001 05665 Pr gt F 00363 lt0001 05665 OUTPUT FOR PROBLEM 3 The GLM Procedure Dependent Variable height Sum of Source DF Squares Mean Square F Value Model 8 1965800000 245725000 5795 Error 15 63600000 04240000 Corrected Total 23 2029400000 RSquare Coeff Var Root MSE height Mean 0968661 3807911 0651153 1710000 Source DF Type III SS Mean Square F Value variety 3 1729200000 576400000 13594 bench 5 236600000 47320000 1116 Level of height variety N Mean Std Dev 1 6 180000000 183084680 2 6 210000000 096540147 3 6 155000000 076681158 4 6 139000000 106395489 Level of height bench N Mean Std Dev 1 4 182000000 325269119 2 4 164000000 257811301 3 4 163000000 310590835 4 4 171500000 340734501 5 4 186000000 310805405 6 4 159500000 340832315 Pr gt F lt0001 Pr gt F lt0001 00001

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