Probability and Statistics > Regression Analysis > Linear Regression Test Value

Linear Regression Test Value

Linear regression test values are used in simple linear regression exactly the same way as test values (like the z-score or T statistic) are used in hypothesis testing, only instead of working with the z-table you’ll be working with a t-distribution table. The linear regression test value is compared to the test statistic to help you support or reject a null hypothesis.

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!

Finding the test statistic

The linear regression test value isn’t much use unless you have something to compare it to. Compare your value to the test statistic. The test statistic is also a t-score (t) defined by the following equation:
t = slope of the sample regression line / standard error of the slope.
See: How to find a linear regression slope / How to find the standard error of the slope (TI-83).

You can find a worked example of calculating the linear regression test value (with an alpha level) here: Correlation Coefficients.

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