Question

EXERCISES 14.3614.50 14.36 Explain why it is preferable to perform a model utility test before using an estimated regression model to make predictions or to estimate the mean y value for specified values of the independent variables Data set available onli Bold exercises answered in back Chapter 14 Multiple Regression Analysis 14-10 a. One of the predictors was xthe distance from the city's major east-west thoroughfare, for which b489 and sb.1044. The model contained seven predictors, and the coefficients were estimated from a sample of 100 vacant lots. Calculate and in- terpret a confidence interval for A, using a confi- dence level of 95% b. Another predictor was x1, an indicator variable for whether the lot was zoned for residential use, for which bl--.183 and %,-.3055. Carry out a test of H°: β1 a: β-0, and interpret the conclusion in the context of the problem = 0 versus H

Answer 1

@ Number of pvedictors, k=7 ctors , Total sample data, n= (00 degrees of fveedom = n-k-1 = 100-7-1=92. significance level , α=-0.95 0.05 .. C í ticak value, t%.- 1.986

95% confidence interval for ß3 <-04g9 + 1986(0-1044) -0. 489-1.986 (0.1044) 乡 963 B3 0 2816

** Interpretation: With 95% confidence, we can say that the tue value os the estimaror A3 Ue bedeen s the inter val doen mot 06963 and - O- 2816 . As the interval doen mot include zero valua, the estimator A3 is not equal to 2ero andhthe predicror X3 is a signi ficant vaviable

Alternative hypothe)is, Hı: ß Test statisic, t- 217PL 13-o O 3 055 S b degreen ot treedom - n-k--1 Condlupion: As ount p-value is large we fail to veject the null hypothenis, Ho and Conclude that athe estimator not difHerent t ZeYo and thun he predicor x, is noto significant Vayiable