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:

A residual is the difference between the observed value of \(y\) and the predicted value of \(y\) from the regression equation (\(e = y-\hat{y}\)). Positive residual means the observed value is greater than the predicted value (regression equation underestimates \(y\)), and negative residual means the observed value is less than the predicted value (regression equation over - estimates \(y\)). At \(x = 6\), the residual is positive, so the regression equation underestimates \(y\). The distribution of positive and negative residuals doesn't clearly show over - estimation is more common. The scatter of residuals doesn't give information about the slope of the regression line. But when \(x = 6\), since the residual is positive (\(y-\hat{y}>0\)), the least - squares regression equation underestimates \(y\), which means the opposite of option A is true.

Answer:

None of the above options are correct.