One way to assess how well a regression model fits a dataset is to calculate the root mean square error, which is a metric that tells us the average distance between the predicted values from the model and the actual values in the dataset.

The lower the RMSE, the better a given model is able to “fit” a dataset.

The formula to find the root mean square error, often abbreviated RMSE, is as follows:

RMSE = √Σ(P_i – O_i)² / n

where:

• Σ is a symbol that represents “sum”
• P_i is the predicted value for the i^th observation in the dataset
• O_i is the observed value for the i^th observation in the dataset
• n is the sample size

The following step-by-step example shows how to calculate the RMSE 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 printdata=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 regdata=exam_data;
    model score = hours;
run;

Step 3: Extract RMSE from Regression Model

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

/*fit simple linear regression model*/
proc regdata=exam_data outest=outest noprint;
    model score = hours / rmse;
run;
quit;

/*print RMSE of model*/
proc printdata=outest;
    var _RMSE_;
run;

Notice that only the RMSE value of 3.64093 is shown in the output.

Note: The argument noprint in proc reg tells SAS not to print the entire output of regression results as it did in the previous step.

The following tutorials explain how to perform other common tasks in SAS: