In the regression equation Y^ = a + bX, what is the regression line?

In the regression equation Y^ = a + bX, what is the regression line?

• A. A line showing the mean of Y.
• B. A line representing the difference between groups.
• C. The regression line is the line Y^ = a + bX that predicts Y from X.
• D. The line that shows causation from X to Y.

Answer: (C)

The regression line in simple linear regression is the line that gives the predicted value of Y for each value of X. It is written as Y-hat = a + bX and represents the mean of Y conditional on X under the model. This line is found by least squares to minimize the squared differences between observed Y and the predicted Y, capturing the overall trend of Y as X changes. It does not reflect causation, nor is it simply a line of differences between groups; it’s a predictive relationship showing how Y tends to vary with X. So the best description is that it predicts Y from X using the equation Y-hat = a + bX.

The regression line in simple linear regression is the line that gives the predicted value of Y for each value of X. It is written as Y-hat = a + bX and represents the mean of Y conditional on X under the model. This line is found by least squares to minimize the squared differences between observed Y and the predicted Y, capturing the overall trend of Y as X changes. It does not reflect causation, nor is it simply a line of differences between groups; it’s a predictive relationship showing how Y tends to vary with X. So the best description is that it predicts Y from X using the equation Y-hat = a + bX.