1. Data from a sample of employees from a large multinational corporation were used to estimate the following least squares regression equation:

Salary = 36775 + 1590 Years of Experience

a)What is the explanatory variable?

b)What is the response variable?

c)What does the slope mean in this context?

d)What does the y-intercept mean in this context? Is it meaningful?

1. Based on the regression equation from the previous exercise,

Salary = 36775 + 1590 Years of Experience,

a.What is the predicted salary for an employee with 10 years of experience?

b.If the salary for an employee with 10 years of experience turned out to be $56,500, what is the residual?

c.What is the predicted salary for an employee with 20 years of experience?

d.If the salary for an employee with 20 years of experience turned out to be $64,550, what is the residual?

1. Based on the following data set and summary statistics:

X

Y

6

20

9

18

12

10

15

8

18

9

25

4

Mean of x = 14.17 Standard deviation of x = 6.79

Mean of y = 11.50 Standard deviation of y = 6.19

Correlation r = -0.920.

a)What is the slope of the estimated regression equation?

b)What is the intercept of the estimated regression equation?

c)What is the predicted value of y when x is 25?

d)What is its residual?

1. Suppose that the correlation, r, between two variables x and y is +0.77.

a.Is the slope of the estimated regression equation relating x and y positive or negative?

b.For an x value that is 1 standard deviation above its mean, how many standard deviations above its mean would you predict the y value to be?

c.What would you predict about a y value if the x value is 2 standard deviations above its mean?

d.What would you predict about a y value if the x value is 2 standard deviations below its mean?

1. Suppose that the correlation, r, between two variables x and y is -0.44.

a)What would you predict about a y value if the x value is 2 standard deviations above its mean?

b)What would you predict about a y value if the x value is 2 standard deviations below its mean?

c)What fraction of the variability in y can be explained by x?

d)What fraction of the variability in y cannot be explained by x?

1. A real estate agency fit a regression equation to determine the length of time a property is on the market (number of months) before it sells based on asking price (in thousands of dollars). The following results were obtained.

Time on Market = -0.64 + .041 Asking Price R2 = 50.5%

a. Interpret the meaning of R2.

b. Is the correlation between Time on Market and Asking Price positive or negative?

How do you know?

c. What is the correlation between Time on Market and Asking Price?

d. What proportion of the variability in Time on Market is not accounted for by Asking Price?