Is CEO compensation related to a company's performance? To test whether CEO compensation and a company's stock performance are related, a financial analyst collected data on 12 randomly selected, publicly traded companies. For each company, the analyst looked at two variables: the percent change in stock price over the past five years (which she denoted x ) and the percent change in CEO compensation over the past five years (which she denoted y ). For these 12 companies, the least-squares regression equation relating the two variables was =y+−0.1650.046x , and the standard error of the slope of this least-squares regression line was approximately 0.028 . Using her information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope β1 . (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) and (e) Based on the information, can we conclude (using the 0.05 level) that there is a significant linear relationship between percent change in stock price over the past five years and percent change in CEO compensation over the past five years? Yes No

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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Question

Is CEO compensation related to a company's performance?

To test whether CEO compensation and a company's stock performance are related, a financial analyst collected data on

randomly selected, publicly traded companies. For each company, the analyst looked at two variables: the percent change in stock price over the past five years (which she denoted

) and the percent change in CEO compensation over the past five years (which she denoted

). For these

companies, the least-squares regression equation relating the two variables was

=y+−0.1650.046x

, and the standard error of the slope of this least-squares regression line was approximately

0.028

Using her information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope

β1

. (Assume that the variable

follows a normal distribution for each value of

and that the other regression assumptions are satisfied.) Use the

0.05

level of significance, and perform a two-tailed test. Then complete the parts below.

(If necessary, consult a list of formulas.)

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	▼(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)

(d)	Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
and
(e)	Based on the information, can we conclude (using the 0.05 level) that there is a significant linear relationship between percent change in stock price over the past five years and percent change in CEO compensation over the past five years?
Yes No

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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