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Linear Regression Test Value: How to Find it

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Linear Regression Test Value

Two linear regression lines.

Two linear regression lines.

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):
linear regression test value

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.

Questions? Post a comment and I’ll do my best to help!

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Linear Regression Test Value: How to Find it was last modified: November 15th, 2016 by Stephanie

5 thoughts on “Linear Regression Test Value: How to Find it

  1. Vanessa DuBarry

    This blog is soooo helpful, just be careful with the numbers. but besides that its not that hard, but this blog sure makes it easier!!

  2. Donna Allen

    This explanation was helpful and easy to understand. I agree that the blog has made things a lot easier to understand.

  3. Tammy Sutton

    Why do you subtract 2? I was wondering that last night when I was working on my homework. I subtracted the two and got the right answer, but I don’t understand why I subtracted the 2.

  4. Alison Bryant

    this was really helpful, I was confused about how to get the value without a test, but now I understand.

  5. William bBverly

    How can I calculate the “Regression Coefficient” (not sure of this name) – the number that reflects the accuracy of the graph line or equation in representing the actual data?

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