"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.
5. Black Cherry Tree Volume The volume (in cubic feet) of a black cherry tree can be modeled by the equation
y =- 52.2+0.3x_1 +4.5x_2
where x_1 is the tree's height (in feet) and x_2 is the tree's diameter (in inches). (Source: Journal of the Royal Statistical Society)
a. x_1 = 70, x_2 = 8.6
b. x_1 = 65, x_2 = 11.0
c. x_1 = 83, x_2 = 17.6
d. x_1 = 87, x_2 = 19.6"

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"

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

6. Elephant Weight The equation used to predict the weight of an elephant (in kilograms) is

y =- 4016+11.5x_1+7.55x_2+12.5x_3

where x_1 represents the girth of the elephant (in centimeters), x_2 represents the length of the elephant (in centimeters), and x_3 represents the circumference of a footpad (in

centimeters). (Source: Field Trip Earth)

a. x_1 = 421, x_2 = 224, x_3 = 144

b. x_1 = 311, x_2 = 171, x_3 = 102

c. x_1 = 376, x_2 = 226, x_3 = 124

d. x_1 =231, x_2 = 135, x_3 = 86"

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

10. y-intercept

a. \hat{y}_i

b. y_i

c. b

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

e. m

f. \bar{y}"

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

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.

27. An equation that can be used to predict fuel economy (in miles per gallon) for automobiles is

y=41.3- 0.004x_1 - 0.0049x_2

where x_1 is the engine displacement (in cubic inches) and x_2 is the vehicle weight (in

pounds).

a. x_1 = 305, x_2 = 3750

b. x_1 = 225, x_2 = 3100

c. x_1 = 105, x_2 = 2200

d. x_1 = 185, x_2 = 3000"

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.

28. Use the regression equation found in Exercise 25.

a. x_1 = 9.0, x_2 = 0.70

b. x_1 = 3.0, x_2 = 0.25

c. x_1 = 8.0, x_2 = 0.60

d. x_1 = 5.2, x_2 = 0.46"