In simple linear regression (as in Excel’s trendline output), the model is written as $y=mx+b$. What do $m$ and $b$ represent?

• A. $m$ is the y-intercept (predicted $y$ when $x=0$), and $b$ is the slope (change in predicted $y$ for a 1-unit increase in $x$).
• B. $m$ is the correlation coefficient $r$, and $b$ is the coefficient of determination $R^2$.
• C. $m$ is the slope (change in predicted $y$ for a 1-unit increase in $x$), and $b$ is the y-intercept (predicted $y$ when $x=0$).
• D. $m$ is the coefficient of determination $R^2$, and $b$ is the p-value for the regression slope.

Answer: (C)

Verified step by step guidance

1. Recall the general form of a simple linear regression equation: \(y = m x + b\), where \(y\) is the predicted value of the dependent variable and \(x\) is the independent variable.
2. Understand that the coefficient \(m\) represents the slope of the regression line. This means \(m\) indicates how much the predicted value of \(y\) changes for a one-unit increase in \(x\).
3. Recognize that the coefficient \(b\) represents the y-intercept of the regression line. This is the predicted value of \(y\) when \(x = 0\).
4. Note that the slope \(m\) tells us the direction and steepness of the relationship between \(x\) and \(y\), while the intercept \(b\) provides a starting point on the \(y\)-axis.
5. Therefore, in the equation \(y = m x + b\), \(m\) is the slope (change in predicted \(y\) for a 1-unit increase in \(x\)), and \(b\) is the y-intercept (predicted \(y\) when \(x = 0\)).