Learn by Doing
Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.
A list of StatCrunch directions is provided at the bottom of this text-box.
Context
The modern Olympic Games have changed dramatically since their inception in 1896. Are athletes getting better? We will use regression to investigate the change in winning times for one event—the men's 1,500 meter race.
Variables
Year: the year of the Olympic Games, from 1896 to 2000. Time: the winning time for the 1,500 meter race, in seconds.
Since the winning time depends on the year, the Year since 1896 is the explanatory variable, and the Winning time is the response variable.
Data
The olympics datafile includes the winning times for the men's 1,500-meter race since 1896. Open the olympics datafile in the Stats at Cuyamaca College group on StatCrunch (directions - opens in a new tab).
Prompt
In the first two questions below, you will use StatCrunch to produce and examine the scatterplot for the olympics datafile. You will also use StatCrunch to find the regression equation and correlation coefficient.
List of StatCrunch Directions
As you work through numbers 1) and 2) below, refer back to these StatCrunch directions when you need a quick reminder.
- Open StatCrunch
- Open a datafile in the Stats at Cuyamaca College group
- Download StatCrunch Output Window (do not take screenshots; please use these directions)
- Embed Pictures in a Textbox (do not post attachments; please use these directions)
- Copy and Paste StatCrunch Text Output
- Produce Scatterplot, LSR Line, Regression Equation, & R (All at the same time!)
Question 1
If you have not done so, open the olympics datafile in the Stats at Cuyamaca College group on StatCrunch (directions - opens in a new tab).
- Using the year since 1896 as the explanatory variable and the winning time as the response variable: graph the scatterplot with the regression line and produce the regression equation with the correlation coefficient - all at the same time (directions)
- Toggle to the output page with the scatterplot and regression line. Notice that the data has a strong linear association, so it makes sense to use linear regression. (Always check the form of the scatterplot before using linear regression.)
- Download the StatCrunch output page with your scatterplot and regression line graphed together. (directions)
- Embed the .png file for your scatterplot and regression line in the text-box below. (directions)
Question 2
These directions assume you have produced the Simple linear regression results in a multipage StatCrunch output window. If not please see the previous question.
- Toggle to the StatCrunch output page with the regression equation, correlation coefficient, and other statistics.
- Under the heading Simple linear regression results, copy and paste the first five lines (dependent variable, independent variable, linear equation, sample size, and R) into the text-box below. (directions)