Stand mixers The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers.35 The mixer from Walmart (highlighted in red) was much lighter—and cheaper than the other mixers.

a. Describe what influence the highlighted point has on the equation of the least-squares regression line.

b. Describe what influence the highlighted point has on the standard deviation of the residuals and r2

We can see that highlighted point in the scatterplot in the question, and we can see that it has a much lower weight and a much lower price than the rest of the individuals in the sample. Because this point is below the predicted regression line that runs through the other points of the scatterplot, it makes the regression line steeper, increasing the slope. Because the point makes the regression line steeper, the intersection of the regression line with the vertical axis at $x=0$ will be lower, and the y-intercept will be lower.

We know that the highlighted point is near the scatterplot's bottom left corner. Because the point is so near to the regression line in the scatterplot, the residual is quite small. The standard deviation of the residual, on the other hand, reflects the amount of variations in the response variables that the least-squares regression line can explain. Because the highlighted point is so close to the least-squares regression line, it looks that when the point is included, there is more variance in the response variables explained by the regression line, and so the point raises the coefficient of determination.