The scatterplot below displays a set of bivariate data along with its leastsquares regression line.

Consider removing the point $(66,15)$ and calculating a new least-squares regression line.

What effect(s) would removing this point have?
Choose all answers that apply:

A The coefficient of determination $\left(r^{2}\right)$ would decrease.
B The standard deviation of the residuals would decrease.
C The correlation coefficient $(r)$ would get closer to -1 .

Question

The scatterplot below displays a set of bivariate data along with its leastsquares regression line.

Consider removing the point $(66,15)$ and calculating a new least-squares regression line.

What effect(s) would removing this point have?
Choose all answers that apply:

A The coefficient of determination $\left(r^{2}\right)$ would decrease.
B The standard deviation of the residuals would decrease.
C The correlation coefficient $(r)$ would get closer to -1 .

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the outlier in the scatterplot. ‖ ‖ step 2 ⋮ Recognize that the point (66,15) lies above the regression line and is an outlier. ‖ ‖ step 3 ⋮ Understand that removing an outlier can affect the regression line, the correlation coefficient, and other statistical measures. ‖ ‖ step 4 ⋮ Predict that removing the outlier will likely result in a regression line that better fits the remaining data points. ‖ ‖ step 5 ⋮ Anticipate that the correlation coefficient $r$ will likely increase in absolute value, getting closer to -1 if the outlier is in the direction of the positive correlation. ‖ ‖ step 6 ⋮ Expect that the standard deviation of the residuals will decrease because the outlier that is contributing to a larger spread of residuals is removed. ‖ ‖ step 7 ⋮ Consider that the coefficient of determination $r^2$ will likely increase, reflecting a better fit of the regression line to the data points without the outlier. ‖ ∻Answer∻ ⚹ B The standard deviation of the residuals would decrease. C The correlation coefficient $(r)$ would get closer to -1. ⚹ ∻Key Concept∻ ⚹Impact of Removing an Outlier on Regression Analysis⚹ ∻Explanation∻ ⚹Removing an outlier from a set of data points can lead to a decrease in the standard deviation of the residuals and an increase in the absolute value of the correlation coefficient, reflecting a stronger linear relationship between the variables.⚹◊What is the formula for calculating the coefficient of determination ($r^2$)?⍭ Generate me a similar question◊

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