In the regression line equation $y=mx+b$ (as used in Excel trendlines), what does $b$ represent?

• A. The y-intercept: the predicted value of $y$ when $x=0$
• B. The coefficient of determination $R^2$, the proportion of variation in $y$ explained by $x$
• C. The correlation coefficient $r$ between $x$ and $y$
• D. The slope: the change in predicted $y$ for a one-unit increase in $x$

Answer: (A)

Verified step by step guidance

1. Recall the general form of the regression line equation: \(y = m x + b\), where \(y\) is the predicted value, \(x\) is the independent variable, \(m\) is the slope, and \(b\) is the y-intercept.
2. Understand that the y-intercept \(b\) represents the predicted value of \(y\) when \(x = 0\). This means it is the point where the regression line crosses the y-axis.
3. Recognize that the slope \(m\) indicates how much \(y\) changes for a one-unit increase in \(x\), but this is different from the y-intercept \(b\).
4. Note that the coefficient of determination \(R^2\) measures the proportion of variation in \(y\) explained by \(x\), and the correlation coefficient \(r\) measures the strength and direction of the linear relationship between \(x\) and \(y\); neither of these are represented by \(b\).
5. Therefore, \(b\) specifically corresponds to the y-intercept, the predicted value of \(y\) when \(x\) equals zero.