Explanation Given info: In the data of 9 custom homes currently listed for sale, the random variable x denotes size in hundreds of square feet and the random variable y denotes price in thousands of dollars. The given level of significance is α = 0.01 . Justification: Standard error of estimate: The residual is defined as e = y ^ − y where y ^ be the predicted value of the response variable and y be the actual value of the response variable. For a set of n observations the standard error of estimate is given as, s e = S S E n − 2 where SSE is the error sum of squares . Standard error of estimate: Software procedure: Step by step procedure to obtain standard error of estimate using Minitab software is given as, Choose Stat > Regression > Fitted Line Plot . In Response ( Y ) , enter the numeric column containing the response data. In Predictor ( X ) , enter the numeric column containing the predictor variable. Click OK . The output using Minitab software is given as, Thus, the standard error of estimate is s e = 59.6208 . The hypotheses are stated as given below: Null hypothesis: H 0 : β 1 = 0 That is, x is not useful for predicting y Alternative hypothesis: H 0 : β 1 ≠ 0 That is, x is useful for predicting y Degrees of freedom: For sample size n the degrees of freedom is n − 2 . Here, the sample size 9 d .f . = n − 2 = 9 − 2 = 7 Thus, the degrees of freedom is 7. Critical value: The level of significance is α = 0.01 α 2 = 0.01 2 = 0.005 From the table IV in Appendix A, critical values for t -test with degrees of freedom as 7 at α 2 = 0.005 is 3.499. Since, t -distribution is symmetric the critical value is ± 3.499 Standard error of estimate: The standard error of estimate is s e given by the formula, S x x = ∑ i x i 2 − ( ∑ i x i ) 2 n . Now, x i y i x i 2 26 540 676 27 555 729 33 575 1,089 29 577 841 29 606 841 34 661 1,156 30 738 900 40 804 1,600 22 496 484 270 5,552 8,316 Thus, for sample size n = 9 , ∑ i x i = 270 , ∑ i x i 2 = 8 , 316

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Author: Neil A. Weiss

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Chapter 15.2, Problem 60E

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Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

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Chapter 15.2, Problem 59E

Chapter 15.2, Problem 61E

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Chapter 15 Solutions

Introductory Statistics (10th Edition)

Ch. 15.1 - Suppose that x and y are predictor and response...Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - In Exercises 15.315.6, assume that the variables...Ch. 15.1 - The difference between an observed value and a...Ch. 15.1 - Identify two graphs used in a residual analysis to...Ch. 15.1 - Which graph used in a residual analysis provides...Ch. 15.1 - Figure 15.8 shows three residual plots and a...

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Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

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Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

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