HW5sol - Stat 512-1 Solutions to Homework #5 Dr. Levine 1....

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Stat 512-1 Solutions to Homework #5 Dr. Levine 1. 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 ) -1 X’Y . (If you have trouble with matrix multiplication, see pages 4-5 of Topic 3.) 1 2 1 4 1 6 1 8 1 10 = X , 1 1 1 1 1 2 4 6 8 10 ′ = X , 1 2 1 4 1 1 1 1 1 5 30 1 6 2 4 6 8 10 30 220 1 8 1 10 = = X X ( 29 1 2 11 3 220 30 1.1 0.15 1 10 20 30 5 3 1 0.15 0.025 5 220 30 20 40 - - - - = = = - - - × - X X 1 2 1 1 1 1 1 1 2 5 7 9 24 5 2 4 6 8 10 2 8 30 56 90 186 7 9       + + + +   = = = + + + +         X Y ( 29 1 1.1 0.15 24 26.4 27.9 1.5 0.15 0.025 186 3.6 4.65 1.05 - - - -   = = = =   - - +   b X X X Y For the following 5 problems use the commercial properties data described in the text with problem 6.18 on page 251 — 252. 2. Run the linear regression with rental rates as the response variable, and all four explanatory variables. Summarize the regression results by giving the fitted regression equation, the value of R 2 , and the results of the significance test for the null hypothesis that the four regression coefficients for the explanatory variables are all zero (give null and alternative hypotheses, test statistic with degrees of freedom, P-value, and a brief conclusion in words). Analys is of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 138.32691 34.58173 26.76 <.0001 Error 76 98.23059 1.29251 Correc ted Tota l 80 236.55750 Root MSE 1.13689 R-Square 0.5847
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Dependent Mean 15.13889 Adj R-Sq 0.5629 Coeff Var 7.50970 Parameter Est imates Parameter Standard Variab le DF Est imate Error t Value Pr > | t | 95% Confidence Limi ts In te rcep t 1 12.20059 0.57796 21.11
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HW5sol - Stat 512-1 Solutions to Homework #5 Dr. Levine 1....

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