17A Coreq

In the next preview assignment and in the next class, you will need to be able to identify response and explanatory variables, check assumptions with residual plots, write a simple linear regression equation, interpret a regression coefficient in the context of the data, and interpret the coefficient of determination.
Review of Simple Linear Regression 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 in a dataset called “PulseRate.” The variables in the dataset 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)
We will be investigating pulse rate in the preview assignment. In this corequisite support activity, we will focus on a different investigative question—the students are interested in building a model that can be used to estimate a student’s weight based on the student’s height. To complete this support activity, you will need to access the DCMPLinear Regression tool at https://dcmathpathways.shinyapps.io/LinearRegression/. You will also need to upload spreadsheet DCMP_STAT_17A_PulseRate into the data analysis tool. To upload a dataset, select “Upload File” under “Enter Data.”Then, click “Browse”to find the location of the file on your computer and click “Open.” The dataset will be uploaded into the data analysis tool.

Question 1

1) What arethe explanatory and response variables?

Question 2

2) Create a scatterplot to visualize the relationship between the explanatory and response variable. Don’t forget to select the explanatory variable (𝑋)and response variable (𝑌)in the data analysis tool.

Question 3

3) Using the scatterplot you created in Question 2, describe the relationship between student weight and student height.

Question 4

4) Fit a linear regression model to describe the relationship between student height andstudentweight. Calculate the line of best fit to describe the relationship between the two variablesusing the data analysis tool. What is the equation of the simple linear regression model?

Question 5

5) Interpret the value of the slope of the line of best fit.

Question 6

6) Create a scatterplot of the residuals vs. weight(𝑥)by selecting the Fitted Values & Residual Analysis tab. Is there anything about this residual plot that would cause you toquestion the reasonableness of fitting a linear model?

Question 7

7) Calculate𝑅2 using the data analysis tooland interpret the value.

Question 8

8) At the 5% significance level, determine whether there is convincing evidence to conclude that there is a useful linear relationship between student height and student weight. Test the hypothesis: 𝐻0:β=0vs. 𝐻𝐴:β≠0. Write your answer in a complete sentence and support your answer with statistical evidence.

  1. Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org.http://www.statsci.org/data/oz/ms212.html ↵