12. Regression

Two variables have a bivariate normal distribution. Explain what this means.

The scatterplot below shows a set of data and its least-squares regression line. Based on the graph, which of the following is most likely the equation of the regression line?

A regional sales manager records data on the number of clients a salesperson contacts in a week (x) and the total sales generated that week (y). The data from 10 salespeople is shown below. Find the equation of the regression line and use it to predict sales if the salesperson contacts (a) 6 clients; (b) 40 clients

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight

loss."

2. Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

5. To predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

7. The y-value of a data point corresponding to x;

a. \hat{y}_i

b. y_i

c. b

d. (\bar{x}, \bar{y})

e. m

f. \bar{y}"

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

9. Slope

a. \hat{y}_i

b. y_i

c. b

d. (\bar{x}, \bar{y})

e. m

f. \bar{y}"

"In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.

12. The point a regression line always passes through

a. \hat{y}_i

b. y_i

c. b

d. (\bar{x}, \bar{y})

e. m

f. \bar{y}"

3. Explain how to predict y-values using the equation of a regression line.

4. For a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

1. Interpret the meaning of the coefficient -8.2 in the multiple regression equation y=112.1+0.43x_1-8.2x_2+29.5x_3.

2. Compare the numbers of dependent and independent variables in a multiple regression equation and a single regression equation.

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.

3. Cauliflower Yield The equation used to predict the annual cauliflower yield (in pounds

per acre) is y=24,791+4.508x_1-4.723x_2

where x_1 is the number of acres planted and x_2 is the number of acres harvested.(Adapted from United States Department of Agriculture)

a. x_1 = 36,500, x_2 = 36,100

b. x_1 = 38,100, x_2 = 37,800

c. x_1 = 39,000, x_2 = 38,800

d. x_1 = 42,200, x_2 = 42,100"

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.

4. Sorghum Yield The equation used to predict the annual sorghum yield (in bushels per

acre) is y = 80.1-20.2x_1 +21.2x_2

where x_1 is the number of acres planted (in millions) and x_2 is the number of acres harvested (in millions). (Adapted from United States Department of Agriculture)

a. x_1 = 5.5, x_2 = 3.9

b. x_1 = 8.3, x_2 = 7.3

c. x_1 = 6.5, x_2 = 5.7

d. x_1 = 9.4, x_2= 7.8"