# 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 Pearsonâ€™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 đť‘ź, 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 doesnâ€™t matter what the slope of this line is. Whether itâ€™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 donâ€™t lie exactly on the line, but they do lie near it, so the correlation coefficient is perhaps 0.8, then again it doesnâ€™t matter how steep the line itself is. Itâ€™s how close to the line the points are that weâ€™re interested in.

The statement is false. A larger value of the correlation coefficient doesnâ€™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.