years Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Question 24 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee The data is reproduced above for this experiment. Please calculate the standard error of the estimate, or s, for the regression

years Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Question 24 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee The data is reproduced above for this experiment. Please calculate the standard error of the estimate, or s, for the regression

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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years Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Question 25 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee Using your excel output from this regression, what is the correct decision using the p value method for the slope test (assume an alpha level of .05) H0: B1 = 0 (not a linear relationship) H1: B1 ≠ 0 (is a linear relationship) a) a. fail to reject the null hypothesis, there is insufficient evidence of a linear relationship b) b. fail to reject the null hypothesis, there is sufficient evidence of…
years Xi bonus Yi XiYi Xi2 4 5.7 22.8 16 2 3.5 7 4 7.4 10.1 74.74 54.76 5 9 45 25 2 2.7 5.4 4 12 12 144 144 Are years of service and annual bonuses related? The annual bonuses of 6 randomly selected employees (measured in “thousands of dollars”) along their their respective years of service for the company. Suppose we estimate a linear regression using the Ordinary Least Squares technique of the form: Bonusi = b0 + b1(yearsi) where the subscript i indicates the ith employee Using excel to complete this problem, what is the numerical value of b1 and its associated p value
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