How to Calculate R-Squared in SAS

R-squared, often written as r², is a measure of how well a linear regression model fits a dataset.

This value represents the proportion of the variance in the response variable that can be explained by the predictor variable.

The value for r² can range from 0 to 1:

A value of 0 indicates that the response variable cannot be explained by the predictor variable at all.
A value of 1 indicates that the response variable can be perfectly explained without error by the predictor variable.

The following step-by-step example shows how to calculate the R-squared value for a simple linear regression model in SAS.

Step 1: Create the Data

For this example, we’ll create a dataset that contains the total hours studied and final exam score for 15 students.

We’ll to fit a simple linear regression model using hours as the predictor variable and score as the response variable.

The following code shows how to create this dataset in SAS:

/*create dataset*/
data exam_data;
    input hours score;
    datalines;
1 64
2 66
4 76
5 73
5 74
6 81
6 83
7 82
8 80
10 88
11 84
11 82
12 91
12 93
14 89
;
run;

/*view dataset*/
proc print data=exam_data;

Step 2: Fit the Simple Linear Regression Model

Next, we’ll use proc reg to fit the simple linear regression model:

/*fit simple linear regression model*/
proc reg data=exam_data;
    model score = hours;
run;

simple linear regression output in SAS

Notice that the R-squared value in the output is 0.8310.

This means 83.1% of the variation in exam scores can be explained by the number of hours studied.

Step 3: Extract R-Squared Value of Regression Model

If you only want to view the R-squared value of this model and none of the other output results, you can use the following code:

/*fit simple linear regression model*/
proc reg data=exam_data outest=outest noprint;
    model score = hours / rsquare;
run;
quit;

/*print R-squared value of model*/
proc print data=outest;
    var _RSQ_;
run;