Calculating and Using the Multiple Regression Line

Overview

Why do we use multiple regression? This statistical technique is used to determine the relative influence of one or more explanatory (independent) variables to the response (dependent) variable. It also allows you to identify if there are outliers in the data. Let’s say you are a medical researcher and you wish to see whether there is a relationship between a person’s age, cholesterol level, and systolic blood pressure. You have several explanatory variables; thus, using a multiple regression would be a good choice to find the relationship to the response variable.

For this discussion, you will find the multiple regression line for the data, calculate the coefficient of determination, and find a predicted y value for a given situation. You will document your findings in your initial post. Finally, you will respond to your classmates.

Instructions

First, read the scenario. Then, you will answer the prompts below. You may calculate the multiple regression line and coefficient of determination by hand. Or, you may use one of the online calculators provided.

• Social Science Statistics Multiple Regression Calculator (Links to an external site.)
• Stats Blue Multiple Regression Calculator (Links to an external site.)

Scenario: A medical researcher wishes to see whether there is a relationship between a person’s age, cholesterol level, and systolic blood pressure. Eight people are randomly selected. The data is listed in the table. First, find the multiple regression equation. Next, determine the coefficient of determination. Then, use the regression equation to predict a person’s blood pressure reading if the person selected is 50 years old with a cholesterol reading of 220.

Please answer these questions!

Thoroughly respond to the following prompts

1. Identify the explanatory variables and response variable for the data.
2. What is the multiple regression equation for the data?
3. What is the coefficient of determination?
4. If a person 50 years old with a cholesterol of 220 is selected, what is that person’s predicted blood pressure reading?

   5.What information does the coefficient of determination provide you? In other words, what does it explain        about the variation?

   6.Would you use the regression equation to predict the blood pressure reading of a person who is 20 years        old? Why or why not? Think about the range of ages of the randomly selected participants.