a. Explanation Given info: The data is given as, x 1 3 4 4 y 8 0 3 1 The equation is y ^ = 9 − 2 x . 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 . From exercise 15.18 it is found that s e = 2.646 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 4 d .f . = n − 2 = 4 − 2 = 2 Thus, the degrees of freedom is 2. Critical value: Here, the level of significance 10% . That is α = 0.10 For two-tailed test, α 2 = 0.1 2 = 0.05 From the table IV in Appendix A, critical values for t -test with degrees of freedom as 2 at α 2 = 0.05 is 2.920. Since, t -distribution is symmetric the critical value is ± 2.920 . The standard error due to predictor x is given by the formula, S xx = ∑ i x i 2 − ( ∑ i x i ) 2 n . Now, x i y i x i 2 1 8 1 3 0 9 4 3 16 4 1 16 12 13 42 Thus, for sample size n = 4 , ∑ i x i = 12 , ∑ i x i 2 = 42 b. To determine Find 90% confidence interval for the slope of the population regression.

10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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Chapter 15.2, Problem 54E

To determine

Decide at the 10% significance level whether the data provide sufficient evidence to conclude that x is useful for predicting y.

To determine

Find 90% confidence interval for the slope of the population regression.

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Chapter 15.2, Problem 53E

Chapter 15.2, Problem 55E

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Decide at the 10% significance level whether the data provide sufficient evidence to conclude that x is useful for predicting y .

Solution Summary: The author evaluates whether the data provide sufficient evidence to conclude that x is useful for predicting y.