where  and  denote the estimates of the line intercept α and slope β, respectively. Given the following data: Y: 11  14  20  19  20                                                               X:   1    2    3    4    5  Calculate the OLS estimates for the simple linear model in equation (1). Estimate the standard error of the regression in equation (1). Compute the regression’s and test whether this is significantly different from zero at 5% and 1% statistical significance levels. You can find the F-test’s critical values in the Tables in the appendix A at the end of the exam paper

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section: Chapter Questions
Problem 18T
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Consider the following model:

, Equation (1)

where  and  denote the estimates of the line intercept α and slope β, respectively.

Given the following data:

Y: 11  14  20  19  20

                                                              X:   1    2    3    4    5 

  1. Calculate the OLS estimates for the simple linear model in equation (1).
  2. Estimate the standard error of the regression in equation (1).
  3. Compute the regression’s and test whether this is significantly different from zero at 5% and 1% statistical significance levels. You can find the F-test’s critical values in the Tables in the appendix A at the end of the exam paper.

           

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