Questions: The vertical distance between an observation on a scatter plot and the least-squares regression line represents prediction error the correlation coefficient the slope of the line the standard error of the estimate

Solution Steps

The vertical distance between an observation on a scatter plot and the least-squares regression line represents the prediction error. This is also known as the residual, which is the difference between the observed value and the value predicted by the regression line.

The question is asking about the vertical distance between an observation on a scatter plot and the least-squares regression line. This distance is a key concept in regression analysis.

In regression analysis, the least-squares regression line is used to predict the value of a dependent variable based on the value of an independent variable. The vertical distance between an observed data point and the predicted value on the regression line is known as the "residual" or "prediction error."

Let's analyze the given options:

• Prediction error: This is the correct term for the vertical distance between an observation and the regression line.
• The correlation coefficient: This measures the strength and direction of a linear relationship between two variables, not the vertical distance.
• The slope of the line: This represents the rate of change of the dependent variable with respect to the independent variable, not the vertical distance.
• The standard error of the estimate: This measures the average distance that the observed values fall from the regression line, but it is not the vertical distance for a single observation.

Final Answer