- Recognize when a linear regression model will fit a given data set.
- Use technology to create scatterplots, find the line of best fit, and find the correlation coefficient.
- Find the estimated slope and [latex]y[/latex]-intercept for a linear regression model.
- Use the line of best fit to predict values.
Crickets can tell us the outside temperature?!
A famous study was conducted by Dr. Pierce in the 1940s on the relationship between the number of chirps made by a striped ground cricket (measured in number of wing vibrations per second) and the surrounding ground temperature (measured in degrees Fahrenheit)[1]. Dr. Pierce wanted to see if it seemed reasonable to predict the temperature based on the number of chirps.
Now, let’s use our statistical tool to generate appropriate scatterplots, the line of best fit, and the correlation coefficient.
We will use the data the scientist collected[2] to help him answer his research question:
Can ground temperature (measured in degrees Fahrenheit) be predicted by the number of chirps the striped ground cricket makes per second measured in number of wing vibrations per second?
Step 1: Under Enter Data, select Enter Own.
Step 2: Name the [latex]x[/latex] (explanatory) and [latex]y[/latex] (response) variables appropriately.
Step 3: Copy and paste the data from the table (make sure the explanatory variable is in the first column and the response variable is in the second column).
Step 4: Under Plot Options, select Regression Line and Submit Data.
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Let’s quickly summarize the list of our data analysis tools for working with linear relationships between bivariate data:
- Use a scatterplot and [latex]r[/latex] to describe direction and strength of the linear relationship.
- Find the equation of the least-squares regression line, [latex]\hat{y} = a+bx[/latex], to summarize the relationship.