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

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.6: Higher-degree Polynomials And Rational Functions
Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...
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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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