Data Matters with SPSS®

Activity 9.2

Section 9.2 proposes that a way to find a line that does a good job estimating y-values from x-values is to find the line that goes through the mean of the y-values at each x-value, if that’s possible.

There are seven steps to testing this claim.

1. Pick two x-values.
2. Have your software select several random y-values for each x-value.
3. Calculate the regression line that goes through the means of the y-values of each x-value.
4. Use your software to calculate the mistakes the estimate makes.
5. Add up all the mistakes the regression line makes.
6. Does the line go through the mean-mean point?
7. Shift the line by changing the slope and check how that affects the sum of the line’s errors.

Here’s how to do these steps.

Step 1: Pick two x-values.

In Variable View of the data editor, enter X as the name of a new variable. Pick two values for x, switch to Data View, and enter several of each for X.

Step 2: Have your software select several random y-values for each x-value.

Use Transform, Compute to create Y. Use one of the random number generators. (They all begin with “rv.”.)

Step 3: Calculate the regression line that goes through the means of the y-values of each x-value.

Click on Analyze, Compare Means. Move X into the Independent List box, and Y into the Dependent List box. Click OK.

Calculate the equation of a line from the mean of Y for one x-value to the mean of the y-values of the other x-value.

Step 4: Use your software to calculate the mistakes the estimate makes.

In the data editor, use Transform, Compute to create a variable, error. For the numeric equation, enter y minus the right side of your regression equation. For example, if your regression equation is “y=3x–2,” then enter y – (3*x–2). Click OK.

Step 5: Add up all the mistakes the regression line makes.

To get the sum of the errors, click on Analyze, then select Descriptive Statistics, Descriptives. Double-click on error. While you’re at it, double-click on X and Y too. Then click on Options, Sum, Continue, OK.

Step 6: Does the line go through the mean-mean point?

The table with the sum of the regression line’s errors includes the mean of X and the mean of Y. Is the mean-mean point on the line described by your regression equation?

Step 7: Shift the line by changing the slope and check how that affects the sum of the line’s errors.

In the data editor, use Transform, Compute and edit the numeric equation for error, changing the slope and/or intercept of the equation. After each change, get the sum of the errors again. How do your changes affect the sum of the errors?