What describes the regression line?

What describes the regression line?

• A. the line that connects data points exactly.
• B. a horizontal line representing the mean of the x-values.
• C. a vertical line representing the y-intercept.
• D. a line on a scatterplot representing the regression model of the relationship between the two variables plotted.

Answer: (D)

The regression line shows the predicted relationship between two variables on a scatterplot. In simple linear regression, we model y as a linear function of x, and the regression line is the graph of that model, reflecting how predicted y changes as x changes (y = β0 + β1x). It’s estimated to best fit the data by minimizing the squared differences between observed values and predictions, capturing the overall trend rather than passing through every point. This matches the option describing a line on a scatterplot representing the regression model of the relationship between the two variables plotted. The other ideas describe lines that wouldn’t represent the regression relationship (a line through all points, a horizontal line at the mean of x, or a vertical line), so they don’t fit as the regression line.

The regression line shows the predicted relationship between two variables on a scatterplot. In simple linear regression, we model y as a linear function of x, and the regression line is the graph of that model, reflecting how predicted y changes as x changes (y = β0 + β1x). It’s estimated to best fit the data by minimizing the squared differences between observed values and predictions, capturing the overall trend rather than passing through every point. This matches the option describing a line on a scatterplot representing the regression model of the relationship between the two variables plotted. The other ideas describe lines that wouldn’t represent the regression relationship (a line through all points, a horizontal line at the mean of x, or a vertical line), so they don’t fit as the regression line.