Video: Interpreting Linear Regression Coefficients in Context

The scores of a class of students in their end-of-year math and physics examinations can be described by the model ๐‘ฆ = 31.8 + 0.43๐‘ฅ, where ๐‘ฅ is the score in math and ๐‘ฆ is the score in physics. What is the interpretation of the value of 0.43 in the model?

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Video Transcript

The scores of a class of students in their end-of-year math and physics examinations can be described by the model ๐‘ฆ equals 31.8 plus 0.43๐‘ฅ, where ๐‘ฅ is the score in math and ๐‘ฆ is the score in physics. What is the interpretation of the value of 0.43 in the model?

First, letโ€™s imagine this model in the ๐‘ฅ๐‘ฆ-plane. We know you couldnโ€™t have a negative physics score or a negative math score. And that means weโ€™ll just be dealing with the quadrant one result: when ๐‘ฅ is zero, ๐‘ฆ equals 31.8. And weโ€™re dealing with a positive slope, where the math score, on average, is the ๐‘ฅ-axis and the physics score, on average, is the ๐‘ฆ-axis.

If we remember our form ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘, we know that the coefficient of ๐‘ฅ, the invariable, represents the slope and the constant ๐‘ represents the ๐‘ฆ-intercept. The slope is the changes in ๐‘ฆ over the changes in ๐‘ฅ. Related to our model, that would be the changes in physics scores over the changes in math scores. The invariable, the coefficient of ๐‘ฅ, in our problem would be 0.43. We could write that 0.43 as a fraction over one.

We could say as the math score increases by one point as we move to the right one place on our graph, the physics score will increase by 0.43. And so, we say for every additional point scored in the math examination, studentsโ€™ scores increased by, on average, 0.43 additional points in their physics examination. And 0.43 is the relationship from the math score to the physics score.

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