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Question Video: Understanding the Link between a Correlation Coefficient and a Regression Line Mathematics • 9th Grade

True or False: The steeper the slope of a regression line, the larger the correlation coefficient between the two variables.

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Video Transcript

True or False: The steeper the slope of a regression line, the larger the correlation coefficient between the two variables.

For a set of bivariate data, the correlation coefficient or Pearson’s product moment correlation coefficient, which we abbreviate to PMCC, quantifies the strength of the linear relationship between the two variables. In terms of a scatter plot of the two variables, it tells us how closely the points follow a straight line. The correlation coefficient, which we often denote as 𝑟, takes values between negative and positive one. A value of negative one indicates that the points lie exactly on a straight line of negative slope. And a value of positive one indicates that the points lie exactly on a straight line of positive slope.

But it doesn’t matter what the slope of this line is. Whether it’s a steep or shallow slope, if the points lie exactly on the line, in this case a line with positive slope, then the value of the correlation coefficient is still equal to positive one. And if the points don’t lie exactly on the line, but they do lie near it, so the correlation coefficient is perhaps 0.8, then again it doesn’t matter how steep the line itself is. It’s how close to the line the points are that we’re interested in.

The statement is false. A larger value of the correlation coefficient doesn’t mean that the regression line is steeper. It just means that the regression line fits the data more closely, and so the points lie closer to the line.

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