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Linear Regression and Correlation: Prediction

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides an overview of Linear Regression and Correlation: Prediction Up one level as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

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The exam scores (xx-values) range from 65 to 75. Suppose you want to know the final exam score of statistics students who received 73 on the third exam. Since 73 is between the xx-values 65 and 75, substitute x=73x=73 into the equation. Then:

y ^ = -173.51 + 4.83 ( 73 ) = 179.08 y ^ =-173.51+4.83(73)=179.08
(1)

We predict that a statistics student who receives a 73 on the third exam will receive 179.08 on the final exam. Remember, do not use the regression equation to predict values outside the domain of xx.

Example 1

Recall the third exam/final exam example.

Problem 1

What would you predict the final exam score to be for a student who scored a 66 on the third exam?

Solution

145.27

Problem 2

What would you predict the final exam score to be for a student who scored a 78 on the third exam?

Solution

78 is outside of the domain of x values (independent variables), so you cannot reliably predict the final exam score for this student.

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