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# HW5 - the four variables based on the four-variable...

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Stat 512-1 Homework #5 Dr. Levine Due Friday, October 16th 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 the vector b = ( X’X ) -1 X’Y . (If you have trouble with matrix multiplication, see pages 4-5 of Topic 3.) X 2 4 6 8 10 Y 1 2 5 7 9 For the following 5 problems use the commercial properties data described in KNNL with problem 6.18 on page 251 — 252. 2. Run the multiple 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). 3. Give 95% confidence intervals (do not use a Bonferroni correction) for regression coefficients of
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Unformatted text preview: the four variables based on the four-variable multiple regression. Describe the results of the hypothesis tests for the individual regression coefficients (give null and alternative hypotheses, test statistic with degrees of freedom, P-value, and a brief conclusion in words). What is the relationship between these results and the confidence intervals? 4. Plot the residuals versus the predicted rental rates and each of the explanatory variables (i.e. 5 residual plots). Are there any unusual patterns? Describe. 5. Examine the assumption of normality for the residuals using a qqplot and histogram. State your conclusions. 6. Predict the rental rate for the following three properties. Provide a 95% prediction interval with each prediction. Property 1 Property 2 Property 3 X1 (age) 4.0 6.0 12.0 X2 (operating expenses and taxes) 10.0 11.5 12.5 X3 (vacancy rates) 0.10 0.32 X4 (total square footage) 80,000 120,000 340,000...
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