How to Find the Coefficient of Determination

Linear Regression 7 Comments

The coefficient of determination is a measure of how well a statistical model is likely to predict future outcomes. The coefficient of determination, r2 is the square of the sample correlation coefficient between outcomes and predicted values. Finding the coefficient of determination takes only three steps!

Step 1: Find the correlation coefficient, r (it may be given to you in the question). Example, r = 0.543.

Step 2: Square the correlation coefficient.
0.5432 = .295

Step 3:Convert the correlation coefficient to a percentage.
.295 = 29.5%

That’s it!

Related posts:

  1. How to Test for Correlation Coefficients
  2. How to Find a Linear Regression Equation
  3. How to Compute Pearson’s Correlation Coefficients
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7 Responses to “How to Find the Coefficient of Determination”

  1. Donna Allen said:

    Dec 02, 09 at 7:39 pm

    In comparing to some of the problems, this just seemed too easy. It’s refreshing to see that not every problem in statistics is a page-long equation. :)

  2. Vanessa said:

    Dec 03, 09 at 10:41 pm

    I agree this example really helped me! and it was easy, Thank God for this!

  3. Donna Allen said:

    Dec 05, 09 at 12:14 am

    Without these examples on the blog, I don’t know how I would have made it through this course. The guided solution in Mathzone was helpful sometimes. Usually, when I needed a step by step explanation I could find it here. I wish there would have been step by step instructions for some of the challenging problems in chapter 8. I think it would be very helpful for future classes to have them for reference.

  4. Tammy Sutton said:

    Dec 07, 09 at 3:31 pm

    I felt like an idiot when I read this…..It’s so much simpler than I made it.

  5. Alison Bryant said:

    Apr 26, 10 at 12:16 pm

    Oh, I finally understand how to get it, but what does it mean?

  6. Nadya Pena said:

    Sep 15, 11 at 11:21 am

    This problem is only easy when the r (correlation coefficient) is given to you cause then the only thing you have to do is square it. However, if you have to calculate it from scratch then god help you because you’re going to have to dip your feet in the land of total sums of squares, error sums of squares, and regression sums of squares. To calculate all of these by hand is also a pain in the ass and it involves a lot of sigmas, y hats, and means. It’s not terribly difficult. In fact, once you get past the lines and lines of formulas, it’s not so bad. Just a matter of plugging in and not messing up. ;)

  7. Stephanie said:

    Sep 27, 11 at 4:51 pm

    Nadya,
    You are correct. However, in elementary stats r is *usually* given to you.
    Stephanie

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