Answer:
(b) Sometimes increases, sometimes decreases, and sometimes leaves unaffected.
The presence of outliers in a regression analysis can have different effects on the value of R2, which is a measure of how well the regression model fits the data.
Sometimes outliers can have a substantial impact on the regression line, leading to a decrease in R2. Outliers that are far away from the general trend of the data can pull the regression line towards them, resulting in a poorer fit and a lower R2 value.
On the other hand, outliers can also have the opposite effect and increase the value of R2. If the outliers are aligned with the general trend of the data, they can improve the fit of the regression line by capturing additional variance in the dependent variable. In this case, the presence of outliers would increase the value of R2.
In some situations, outliers may have a minimal effect on R2. If the outliers are relatively close to the overall trend of the data, their influence may be limited, and R2 may remain largely unaffected.
Therefore, the presence of outliers can lead to different outcomes for R2, sometimes increasing it, sometimes decreasing it, and sometimes leaving it unaffected.
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