I'm stuck on a homework problem and I'm hoping you all might be able to help me out. I'd be very appreciative!

We were given this data set: Data. I ran a regression in Minitab with GPA as the response and IQ and Self-Concept as the predictors. I've answered a number of questions correctly with this regression, but I can't figure out how to interpret the data to answer the following two questions:

  1. What percent of the variation in GPA is explained by IQ?
  2. Additional amount of variation explained due to the addition of Self-Concept to the model?

This is what I got from Minitab:

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Is this enough information to discern the answer to these questions? If so, how do I interpret this information to find the percent of variation explained by each predictor?

  • $\begingroup$ You have been given enough information there to answer the questions. See of the discussion of sequential sums of squares here, and note how proportion of variation explained relates to regression sums of squares here $\endgroup$ – Glen_b Apr 29 '14 at 23:50

You will want to calculate the Coefficient of Determination (wiki link: http://en.wikipedia.org/wiki/Coefficient_of_determination) which is the fraction of variance explained by your regression divided by the total variance in the data. So if you have r^2 = 1 then 100% of the variance is explained by your model.

To calculate this value you will want to take the Sum of Squares for your regression (in your case 221.58) and then divide it by the Total Sum of Squares (in your case this is 339.43).

So to address your first question you should run a regression using only the IQ variable and get the Sum of Squares for the regression and from that you can calculate the fraction of variance you've explained with your model. I have not used Minitab before but I suspect that this will be equivalent to the Seq SS for the IQ variable (or 143.7)

For your second question you just need to figure out (from your output) what the explained variation is (i.e., 221.58/339.43 or ~65.3%).

I hope that helps.


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