Data Matters with SPSS®

Activity 9.3

Now that there is computer software to do all the computational steps of calculating a regression equation, very few people calculate regression equations by hand. You might wonder whether the calculations in Section 9.3 of Data Matters (or your calculations for the exercises) are correct. To double-check them, you can enter the data into SPSS and compare your answers with SPSS’s.

Once your data are entered in the data editor, you get a regression model by clicking on Analyze, then selecting Regression, Linear.

SPSS calls the x-axis variable Independent and the y-axis variable Dependent. This is because when you create a scatter plot, the tradition is that if you have any suspicions about the direction of causation, you put the cause on the x-axis. On the y-axis, you put the outcome that is dependent on the x-axis variable.

Part of the output will be a table like this.

The slope is the B of your x-axis variable, and its standard error is immediately to its right.

Here are the steps for this part of the project.

1. Find the slope of a relationship between two numeric attributes in the population.
2. Take a sample.
3. Calculate the regression equation and standard error.
4. Check and record whether the confidence interval based on the sample’s slope included the population’s slope.

Repeat the steps to check a number of confidence intervals for the population’s slope.

Step 1: Find the slope of a relationship between two numeric attributes in the population.

Open the Rep US Sample. Find the slope in the population.

Step 2: Take a sample.

In the data editor, click on Data, then select Select Cases, Random Sample of Cases, Sample. Click on Exactly and enter the sample size you want and 50000, so the sentence reads “Exactly [your sample size] cases of the first 50000 cases.“

Step 3: Calculate the regression equation and standard error.

For each new sample, find the slope and standard error.

Step 4: Check and record whether the confidence interval based on the sample’s slope included the population’s slope.

Add and subtract two standard errors. Does your sample include the population slope? Record the slope, its standard error, and the confidence interval.

Repeat these steps to gather more slopes. How often did your confidence interval include the population’s slope?

Try different sample sizes. Does the sample size influence how well the confidence interval works?

How does the standard deviation of the samples’ slopes compare with the estimated standard error of the slope that you got in your first sample?