Preparing for the next classIn the next class, you will need to be able to interpret a linear regression model with two explanatory variables and visualize an interaction between a continuous explanatory variable and a categorical explanatory variable using a scatterplot.In this preview assignment, you will be using spreadsheet DCMP_STAT_17A_PulseRate. For easy reference, here is the background on the data again:Students in an introductory statistics class at The University of Queensland participated in a simple experiment.[1] The students took their own pulse rates. They were then asked to flip a coin. If the coin came up heads, they were to run in place for one minute. Otherwise, they sat for one minute. Afterward, everyone took their pulse rates again. The pulse rates and other physiological and lifestyle data were recorded. There are a total of 110 observations and 11 variables. The variables are:
| Variable | Description |
| ID | Identification number |
| Height | Height in centimeters (cm) |
| Weight | Weight in kilograms (kg) |
| Age | Age in years |
| Sex | Male/female |
| Smokes | Are you a regular smoker? (yes/no) |
| Alcohol | Are you a regular drinker? (yes/no) |
| Exercise | What is your frequency of exercise? (low, moderate, high) |
| GroupAssignment | Whether the student ran or sat between the first and second pulse measurements |
| Pulse1 | First pulse measurement (rate per minute) |
| Pulse2 | Second pulse measurement (rate per minute) |
| Year | Year of class (1993–1998) |
Questions 1–8: The research question that we are interested in exploring is, “How does Pulse1 depend on the weight of the student and their frequency of exercise?”
Question 1
1) What is the response variable?
a) Pulse1
b) Weight
c) Height
d) Exercise
Question 2
2) What variables are the explanatory variables?
a) Pulse1and Weight
b) Pulse1and Height
c) Exerciseand Weight
d) Exerciseand Height
Go to the DCMPExplore Multivariate Relationships tool at https://dcmathpathways.shinyapps.io/MultivariateRelationship/, select “Upload Data,” and upload spreadsheet DCMP_STAT_17A_PulseRate.
Question 3
3) What is the appropriate variable to put in the 𝑥-variable spot in the data analysis tool?
a) Weight
b) Height
c) Pulse1
d) Exercise
Question 4
4) What is the appropriate variable to put in the grouping spot in the data analysis tool?
a) Weight
b) Height
c) Pulse1
d) Exercise
Question 5
5) Click on “Show Linear Regression Equation(s)” in the data analysis tool. Based on the linear regression equations, which level of frequency of exercise increases the first pulse measurement for each one-kilogramincrease in weight?
a) High
b) Low
c) Moderate
d) No level
Question 6
6) Click on “Show Correlation and r2” in the data analysis tool. What would be the correct interpretationof the correlation between Pulse1and Weightfor the high frequencylevel ofexercise?
a) There is a moderate, negative linear relationship between Pulse1and Weightfor students witha high frequency level of exercise.
b) There is no relationship between Pulse1and Weightfor students witha high frequency level of exercise.
c) There is a strong, positive linear relationship between Pulse1and Weightfor students witha high frequency level of exercise.
d) There is a moderate, negative linear relationship between Pulse1and Weightfor all students.
Question 7
7) In the data analysis tool, you can hover over the points in the scatterplot to get their observation numbers. What is the observation number for the student who has a high Pulse1rate compared to the other students and a Weightof around 80 kg?
a) 106
b) 73
c) 91
d) 61
Question 8
8) Determine whether this statement is true or false: In this model, the estimated effect on the initial pulse rate (Pulse1) of a one-kilogramincrease in weight is the SAME for low, moderate,and high exercise rates. Hint: Interpret the estimated coefficient for Weightfor low and then for high. For every one-kilogram increase in the weight of someone who has a LOW level of exercise, we expect the pulse rate to increase by 0.123. For every one-kilogram increase in the weight of someone who has a HIGH level of exercise, we expect the pulse rate to decrease by 0.429.
An interaction occurs when an explanatory variable has a different effect on the response variable, depending on the values of another explanatory variable. An interaction term is a variable that represents an interaction between two variables.
Question 9
9) Do you think an interaction term that looks at the relationship between Weight and Exercise would be appropriate to investigate in a multiple linear regression model? That is, do you think that the level of exercise changes the effect of weight on the initial pulse rate?
a) Yes
b) No
- Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org. http://www.statsci.org/data/oz/ms212.html ↵
