Linear Regression Test Value: Steps

Sample question: Given a set of data with sample size 8 and r = 0.454, find the linear regression test value.

Note: r is the correlation coefficient.

Step 1: Find r, the correlation coefficient, unless it has already been given to you in the question. In this case, r is given (r = .0454). Not sure how to find r? See: Correlation Coefficient for steps on how to find r.

Step 2: Use the following formula to compute the test value (n is the sample size):

How to solve the formula:

1. Replace the variables with your numbers:
   T = .454√((8 – 2)/(1-[.454]² ))
   • Subtract 2 from n:
     8 – 2 = 6
   • Square r:
     .454 × .454 = .206116
   • Subtract step (3) from 1:
     1 – .206116 = .793884
   • Divide step (2) by step (4):
     6 / .793884 = 7.557779
   • Take the square root of step (5):
     √7.557779 = 2.74914154
   • Multiply r by step (6):
     .454 × 2.74914154 = 1.24811026

The Linear Regression Test value, T = 1.24811026

That’s it!