How to Calculate Prediction Interval in Sas

Prediction intervals in SAS provide a range of values within which a future observation is expected to fall, accounting for both the variability in the data and the uncertainty in the prediction. This guide explains how to calculate prediction intervals using SAS procedures, including the PROC REG and PROC GLM procedures.

What is a Prediction Interval?

A prediction interval is an estimate of the range within which a future observation is expected to fall. Unlike confidence intervals, which estimate the range of a population parameter, prediction intervals account for both the variability in the data and the uncertainty in predicting individual observations.

Prediction intervals are particularly useful in regression analysis when you want to predict the value of a dependent variable for a given set of predictor variables. The width of the prediction interval depends on the confidence level you choose and the variability in your data.

How to Calculate Prediction Interval in SAS

SAS provides several procedures for calculating prediction intervals, including PROC REG and PROC GLM. Below are the steps to calculate prediction intervals using these procedures.

Using PROC REG

PROC REG is a general linear regression procedure that can be used to calculate prediction intervals. Here's an example of how to use PROC REG to calculate a 95% prediction interval:

proc reg data=your_dataset; model dependent_variable = predictor1 predictor2; output out=prediction_intervals p=prediction lower=lower upper=upper; run;

In this example:

your_dataset is the name of your SAS dataset.
dependent_variable is the variable you want to predict.
predictor1 and predictor2 are the predictor variables.
p=prediction creates a column with the predicted values.
lower=lower and upper=upper create columns with the lower and upper bounds of the prediction interval.

Using PROC GLM

PROC GLM is another SAS procedure that can be used to calculate prediction intervals. Here's an example of how to use PROC GLM to calculate a 95% prediction interval:

proc glm data=your_dataset; model dependent_variable = predictor1 predictor2; output out=prediction_intervals predicted=prediction lower=lower upper=upper; run;

In this example:

your_dataset is the name of your SAS dataset.
dependent_variable is the variable you want to predict.
predictor1 and predictor2 are the predictor variables.
predicted=prediction creates a column with the predicted values.
lower=lower and upper=upper create columns with the lower and upper bounds of the prediction interval.

Note: The prediction intervals calculated using PROC REG and PROC GLM will be the same if the same model and data are used. The choice between these procedures depends on your specific needs and the type of analysis you are performing.

Worked Example

Let's consider a simple example where we want to predict the weight of a person based on their height. We'll use the following data:

Height (cm)	Weight (kg)
160	55
165	60
170	65
175	70
180	75

We'll use PROC REG to calculate a 95% prediction interval for a person who is 172 cm tall.

proc reg data=weight_data; model weight = height; output out=prediction_intervals p=prediction lower=lower upper=upper; run;

The output will include the predicted weight and the lower and upper bounds of the prediction interval for each observation. For a person who is 172 cm tall, the predicted weight might be 66 kg, with a 95% prediction interval of 62 kg to 70 kg.

Frequently Asked Questions

What is the difference between a confidence interval and a prediction interval?

A confidence interval estimates the range of a population parameter, such as the mean, while a prediction interval estimates the range within which a future observation is expected to fall. Prediction intervals are wider than confidence intervals because they account for additional uncertainty in predicting individual observations.

How do I choose the confidence level for my prediction interval?

The confidence level is typically chosen based on the desired level of certainty. Common choices are 90%, 95%, and 99%. A higher confidence level results in a wider prediction interval, providing more certainty but less precision.

Can I calculate prediction intervals for non-linear models in SAS?

Yes, SAS provides procedures such as PROC NLIN and PROC GENMOD for non-linear models. These procedures can be used to calculate prediction intervals for non-linear models as well.