Question

The given data represent the total compensation for 10 andomly selected CEOs and their company's stock performance in 2009 Analysis of this data reveals a correlation coefficient of r=-0.1876 what would be the predict stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million? 囲Click the icon to view the compensation and stock performance data Click the icon to view a table of critical values for the correlation coefficient. What would be the predicted stock return for a company whose CEO made $15 million? % (Type an integer or decimal rounded to one decimal place as needed.)

Answer 1

Ans) Here we need to predict stock return based on CEO.So here stock return is dependent variable and CEO is independent variable. Let the regression line be : $y_i=\beta_0+\beta_1*x_i + e_i$ , where
i = 1(1)10
and errors
e,S
are normal variates with homoscedastic variance. Now here it is given the data and correlation coefficient between the two variables. The relation between
β1
( the estimator of
61
) and is given by: $\hat\beta_1=r*\frac{s_y}{s_x}$ , where $s_y$ is the sample standard deviation of y and $s_x$ is the sample standard deviation of x. Here
Sy 25.1 4683
and
= 5.458811
and
-0.1876
. So the value of
31 =一0.8642076
. Now $\hat\beta_0$ (the estimator of $\beta_0$ ) is given by : $\hat\beta_0=\bar{y}-\beta_1*\bar{x}$ where $\bar{y}$ is the sample mean of y and $\bar{x}$ is the sample mean of x. Here
y 17.228
and
T16.8
.So the value of
30 31.7466871
.

Now the predicted line is given by:

у + β1 * 2-31.7466871-0.8642076 * 2.

Now put
15
and we get
У 18.78357 18.8
upto one decimal approximation  and put
r25
and we get  
y= 10.1415