a. Explanation Given info: The data is given as, x 0 2 2 5 6 y 4 2 0 –2 1 The equation is y ^ = 2.875 − 0.625 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 15.21 it is found that s e = 1.88193 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 5 d .f . = n − 2 = 5 − 2 = 3 Thus, the degrees of freedom is 3. 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 3 at α 2 = 0.05 is 2.353. Since, t -distribution is symmetric the critical value is ± 2.353 . 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 0 4 0 2 2 4 2 0 4 5 2 25 6 1 36 15 9 69 Thus, for sample size n = 5 , ∑ i x i = 15 , ∑ i x i 2 = 69 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 57E

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 56E

Chapter 15.2, Problem 58E

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You are testing the null hypothesis that there is no linear relationship between two variables, X and Y. From your sample of n=18,you determine that b1=4.6 and Sb1=1.9. c. Based on your answers to (a) and (b), what statistical decision should you make? d. Construct a 95% confidence interval estimate of the population slope, β1.

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

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