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. Age Cholesterol level Blood pressure Person 1 38 220 116 Person 2 41 225 120 Person 3 45 200 123 Person 4 48 190 131 Person 5 51 250 142 Person 6 53 215 145 Person 7 57 200 148 Person 8 61 170 150 Discussion Prompts Show your work: What is the multiple regression equation for the data? What is the coefficient of determination? If a person 50 years old with a cholesterol of 220 is selected, what is that person’s predicted blood pressure reading?
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.
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.
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.
| Age | Cholesterol level | Blood pressure | |
| Person 1 | 38 | 220 | 116 |
| Person 2 | 41 | 225 | 120 |
| Person 3 | 45 | 200 | 123 |
| Person 4 | 48 | 190 | 131 |
| Person 5 | 51 | 250 | 142 |
| Person 6 | 53 | 215 | 145 |
| Person 7 | 57 | 200 | 148 |
| Person 8 | 61 | 170 | 150 |
Discussion Prompts
Show your work:
- What is the multiple regression equation for the data?
- What is the coefficient of determination?
- If a person 50 years old with a cholesterol of 220 is selected, what is that person’s predicted blood pressure reading?
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