*31*

Linear regression is a method we can use to understand the relationship between one or more predictor variables and a response variable.

Typically when we perform linear regression, weâ€™re interested in estimating the mean value of the response variable.

However, we could instead use a method known as **quantile regression** to estimateÂ *any* percentile value of the response value such as the 30th percentile, 90th percentile, 98th percentile, etc.

To perform quantile regression in SAS we can use the **proc quantreg** statement.

The following example shows how to perform quantile regression in SAS in practice.

**Example: Performing Quantile Regression in SAS**

Suppose we have the following dataset in SAS that shows the number of hours studied and corresponding exam score for students in some class:

**/*create dataset*/
data original_data;
input hours score;
datalines;
1 75
1 79
2 78
2 83
2 85
3 84
3 84
3 89
4 93
4 88
4 79
4 94
5 96
5 98
;
run;
/*view dataset*/
proc print data=original_data;
**

Next, weâ€™ll fit a quantile regression model using hours studied as the predictor variable and exam score as the response variable.

Weâ€™ll use the model to predict the expected 90th percentile of exam scores based on the number of hours studied:

/*perform quantile regression*/ proc quantreg data=original_data; model score = hours / quantile = 0.9; run;

From the output, we can see the estimated regression equation:

90th percentile of exam score = 76 + 4.5(hours)

For example, the 90th percentile of scores for all students who study 2 hours is expected to be 85:

90th percentile of exam score = 76 + 4.5*(2) = **85**.

The output also displays a scatter plot of the raw data with the fitted regression line overlaid on the plot:

Unlike a typical regression model, the fitted line for this regression model goes through the 90th percentile of each value of the predictor variable instead of the mean value.

**Additional Resources**

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

How to Perform Simple Linear Regression in R

How to Perform Multiple Linear Regression in R

How to Perform Quadratic Regression in R