Question

the graph displays a residual plot that was constructed after running a least - squares regression on a set of bivariate numerical data (x, y). what can you conclude from this graph? choose 1 answer: a when x = 6, the least squares regression equation overestimates y. b the slope of the least - squares regression line is 0. c the least squares regression equation overestimates y more often than it underestimates y.

Explanation:

Step1: Recall residual concept

Residual = Observed - Predicted. Positive residual means observed > predicted, negative means observed < predicted.

Step2: Analyze \(x = 6\)

At \(x = 6\), the residual is positive. So Observed \(y\) value is greater than the predicted \(y\) - value by the least - squares regression equation. That is, the least - squares regression equation underestimates \(y\) at \(x = 6\), so option A is wrong.

Step3: Analyze slope

The residual plot does not give information about the slope of the least - squares regression line. A non - zero slope is still possible for the regression line, so option B is wrong.

Step4: Count positive and negative residuals

There are more negative residuals than positive residuals. So the least - squares regression equation overestimates \(y\) more often than it underestimates \(y\).

Answer:

C. The least squares regression equation overestimates \(y\) more often than it underestimates \(y\).