a. Explanation Given info: The data represents the result of multiple regressions for hypothetical data collected for n = 30 years. Calculations: The hypothesis for the β 1 is, Null hypothesis : H 0 : β 1 = 0 Alternative hypothesis : H a : β 1 ≠ 0 The test statistic is, t = β ^ 1 s β ^ 1 = 0.03 0.006 = 5 The degrees of freedom is, n − ( k + 1 ) = 29 − ( 5 + 1 ) = 23 Critical value: The rejection region requires α = 0.025 in each tail of the t-distribution, 1. In the column locate the df as 23. 2. In the row locate the level of significance at 0.025. 3. The row and column intersection point is 2.069 is the critical value. Rejection region: If t < − 2.069 or t > 2.069 , then reject the null hypothesis ( H 0 ) . Decision: It is clear that the test value is 5 and the critical value is 2.069. Here, the test value is not less than the critical value. That is, t c a l ( = 5 ) >t 0.05 ( = 2.069 ) . Therefore by the rejection region, reject the null hypothesis. After adjusting all the other values there is sufficient evidence to indicate that there is a linear relationship between vintage year and the logarithm price at α = 0.05 . The hypothesis for the β 2 is, Null hypothesis : H 0 : β 2 = 0 Alternative hypothesis : H a : β 2 ≠ 0 The test statistic is, t = β ^ 2 s β ^ 2 = 0.60 0.120 = 5 Rejection region: If t < − 2.069 or t > 2.069 , then reject the null hypothesis ( H 0 ) . Decision: It is clear that the test value is 5 and the critical value is 2.069. Here, the test value is not less than the critical value. That is, t c a l ( = 5 ) >t 0.05 ( = 2.069 ) . Therefore by the rejection region, reject the null hypothesis. After adjusting all the other values there is sufficient evidence to indicate that there is a linear relationship between average growing season temperature and the logarithm price at α = 0.05 . The hypothesis for the β 3 is, Null hypothesis : H 0 : β 3 = 0 Alternative hypothesis : H a : β 3 ≠ 0 The test statistic is, t = β ^ 3 s β ^ 3 = − 0 b. To determine To interpret: Each of the β estimates. c. To determine To Interpret : The values of R 2 and s . To Describe : whether the model is useful for predicting or not.

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Chapter 12.3, Problem 12.23ACA

To determine

To test: The significance of each of the β parameters.

To determine

To interpret: Each of the β estimates.

To determine

To Interpret: The values of R2 and s.

To Describe: whether the model is useful for predicting or not.

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Chapter 12.3, Problem 12.22ACI

Chapter 12.3, Problem 12.24ACA

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To test: The significance of each of the β parameters.

Solution Summary: The author explains that the data represents the result of multiple regressions for hypothetical data collected for n=30 years.

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To test: The significance of each of the β parameters.

To interpret: Each of the β estimates.

To Interpret: The values of R2 and s. To Describe: whether the model is useful for predicting or not.

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Chapter 12 Solutions

To Interpret: The values of R2 and s.

To Describe: whether the model is useful for predicting or not.