1. Question: In which of the following situations can multiple regression be performed? Select all that apply.
2. Question: In which of the following situations can multiple regression be performed? Select all that apply.
3. Question: Dylan is a graduate student in agricultural studies who is trying to find an equation that relates the yearly soybean yield (in bushels per acre) with the number of acres planted, the number of acres harvested, and the price per bushel of soybeans. What is the correct format for a multiple regression equation?
4. Question: Abby, a real estate agent, is looking to determine how the monthly rent for an apartment is related to its area in square meters and the distance from a mass transit station, in kilometers. What is the correct format for a multiple regression equation?
5. Question: A real estate agent wants to determine how the sale prices of houses y, in thousands of dollars, in a certain city are related to the area, x1, in square feet, the number of bedrooms, x2, and the age of each house, x3, in years. The multiple regression equation that she obtained is shown below. yˆ=403.15+0.043x1+28.241x2−1.028x3
6. Predict the cost, in thousands of dollars, of a 40-year-old house with 1,416 square feet and 2 bedrooms, rounding to one decimal place as needed.
7. Question: Noah is a college dean who is trying to find an equation that predicts the annual cost, y, in dollars, for a university's undergraduate tuition, given the number of undergraduates, x1; the undergraduates' average high school GPA, x2; and the number of undergraduate programs, x3. Noah obtains the multiple regression equation yˆ=4,561−0.163x1+1,853x2+8.695x3. Predict the annual cost of undergraduate tuition at a public university with 8,400 undergraduates, an average high school GPA of 3.31, and 106 undergraduate degree programs. Round to the nearest whole dollar.
8. Question: An educational consultant wants to predict the annual salary of teachers in a school district, y, in thousands of dollars, given the number of years of experience teaching, x1, and the number of years of education, x2. She obtains the multiple regression equation yˆ=44.023+0.299x1+0.386x2. Predict the annual salary of a teacher, in thousands of dollars, with 6 years of experience and 20 years of education. Round to three decimal places as needed.
9. Question: A researcher wants to predict the college grade point averages (GPAs) y of students, given their high school GPA, x1, their score on a standardized test x2 out of 40 points, and the number of colleges to which the student was accepted, x3. She obtains the multiple regression equation yˆ=2.94+0.031x1+0.016x2+0.011x3. Predict the college GPA of a student who was accepted to 11 colleges, with a high school GPA of 3.85, and a standardized test score of 39, rounding to two decimal places.
10. Question: A track-and-field coach wants to predict the 400-meter dash time of an athlete y, given their times in the 200-meter dash x1 and the 400-meter hurdles x2. She obtains the multiple regression equation yˆ=80.51−1.07x1−0.15x2. Predict the 400-meter dash time for an athlete with a 200-meter dash time of 21.93 seconds and a 400-meter hurdles time of 52.85 seconds, rounding to the nearest hundredth of a second.
11. Question: A cardiologist wants to predict the resting heart rate in beats per minute (bpm) of adult males, y, given their age, x1, in years and weight, x2, in pounds. She obtains the multiple regression equation yˆ=43.25+0.779x1+0.0155x2. Predict the resting heart rate of a 40-year-old male who weighs 170 pounds. Round to the nearest whole number.
12. Question: In which of the following situations can multiple regression be performed? Select all that apply.
13. Question: In which of the following situations can multiple regression be performed? Select all that apply.
14. Question: In which of the following situations can multiple regression be performed? Select all that apply.
15. Question: In which of the following situations can multiple regression be performed? Select all that apply.
16. Question: In which of the following situations can multiple regression be performed? Select all that apply.
17. Question: In which of the following situations can multiple regression be performed? Select all that apply.
18. Question: Sarah is a biologist who wants to determine how the life expectancy of a 30-year-old male in a certain region is related to his weight (in kilograms), average daily intake of sodium (in milligrams), and average daily number of cigarettes smoked. What is the correct format for a multiple regression equation?
19. Question: A city planner wants to determine how the rate of violent crime per 100,000 people in a county is related to the population density of the county (in persons per square mile) and the median annual household income in the county. What is the correct format for a multiple regression equation?
20. Question: A real estate agent wants to determine how the sale price of houses in a city are related to the area, in square meters, the number of bedrooms, and the age of each house, in years. What is the correct format for a multiple regression equation?
21. Question: A video game blogger wants to determine how the number of units sold for a new computer game is related to its production budget, its review score (on a 100-point scale), and its marketing budget. What is the correct format for a multiple regression equation?
22. Question: In which of the following situations can multiple regression be performed? Select all that apply.
23. Question: In which of the following situations can multiple regression be performed? Select all that apply.

Multiple Regression

A multiple regression model is a regression model in which more than one independent variable is used to predict the value of one dependent variable. Example 1: Determining if Multiple Regression Can Be Performed

1. Question: A researcher wants to predict home sales prices in thousands of dollars using the square footage of the house, the number of bedrooms, and the age of the house. Can multiple regression be performed? Example 2: Determining if Multiple Regression Can Be Performed
2. Question: A researcher wants to predict the duration of a person's daily commute in minutes using the distance between the person's residence and his or her workplace in miles. Can multiple regression be performed? Example 3: Determining if Multiple Regression Can Be Performed
3. Question: A human resources manager for a business is studying whether some employees are underpaid compared to other employees with comparable experience and performance. She wants to predict the annual salary of an employee, given his or her tenure at a company (in years), amount of secondary education (in years), and performance rating (out of 100 points) on his or her most recent performance review. Can multiple regression be performed?

Key Terms

• Predictor variable:

• Dependent variable:

• Multiple regression equation:

Multiple Regression Equation

A multiple regression equation or model for k independent variables x1, x2, x3, ..., xk and a dependent variable y has the following form, where yˆ is the predicted value of the dependent variable for the given xi values, b0 is the y-intercept, and each coefficient bi is the change in yˆ when the independent variable xi is increased by 1 unit, holding the effects of all of the other independent variables constant.

Example: Writing the Regression Equation

1. Question: An agricultural scientist wants to predict the banana yield per acre of land, y (in tons), using the average rainfall in meters, x1, and the average temperature in Kelvin, x2. What will be the format of the multiple regression equation?
2. Question: In which of the following situations can multiple regression be performed? Select all that apply.
3. Question: In which of the following situations can multiple regression be performed? Select all that apply.
4. Question: In which of the following situations can multiple regression be performed?  Select all that apply.
5. Question: In which of the following situations can multiple regression be performed? Select all that apply.
6. Question: A researcher wants to determine how the current population of a city is related to its population 5 years ago, its population 10 years ago, and its population 15 years ago. What is the correct format for a multiple regression equation?
7. Question: Micah is a financial analyst looking to find how a company's stock price is related to its stock prices for each of the previous four trading days. What is the correct format for a multiple regression equation?
8. Question: Lindsey is the manager of a manufacturing plant. She wants to determine how an employee's productivity rating over time (on a 100-point scale) is related to the number of years of experience and the amount of coffee the employee drinks per day, in ounces. What is the correct format for a multiple regression equation?
9. Question: A superintendent wants to determine how the graduation rates of high schools are related to the average GPA of students at the school and the average score of the school's students on a standardized test. What is the correct format for a multiple regression equation?

10. Question: In which of the following situations can multiple regression be performed? Select all that apply.
11. Question: In which of the following situations can multiple regression be performed? Select all that apply.
12. Question: A track-and-field coach wants to predict the 400-meter dash time (in seconds) of an athlete y, given his or her times (in seconds) for the 200-meter dash x1, the 400-meter hurdles x2, and the 800-meter run x3. She obtains the multiple regression equation yˆ=100.51−1.07x1−0.15x2−0.17x3. Predict the 400-meter dash time of an athlete with a 200-meter dash time of 21.93 seconds, a 400-meter hurdles time of 52.85 seconds, and an 800-meter run time of 109.26 seconds, rounding to the nearest hundredth of a second.
13. Question: A real estate agent wants to determine how the sale prices of houses y, in thousands of dollars, in a certain city are related to the area, x1, in square feet, the number of bedrooms, x2, and the age of each house, x3, in years. The multiple regression equation that she obtained is shown below. yˆ=403.15+0.043x1+28.241x2−1.028x3  Predict the cost, in thousands of dollars, of a 40-year-old house with 1,416 square feet and 2 bedrooms, rounding to one decimal place as needed.
14. Question: Yvette is a veterinarian who wants to find an equation that relates the weight, in pounds, of a cat with its age, in years; its length, in inches; and its average daily intake of cat food, in calories. What is the correct format for a multiple regression equation?
15. Question: Colin is an insurance adjuster who wants to determine how a driver's automotive insurance monthly premiums are related to the number of miles driven per week; the age of the car, in years; and the number of accidents in which the driver has been involved in the past 5 years. What is the correct format for a multiple regression equation?
16. Question: In which of the following situations can multiple regression be performed? Select all that apply.