Question

What effect will this point have on the value of r2 if it is not included in the data?

1) The value of r2 would not be affected because the residual is negative.
2) The value of r2 would not be affected because this point follows the pattern of the data.
3) The value of r2 would increase substantially because this point does not follow the pattern of the data.
4) The value of r2 would decrease substantially because this point does not follow the pattern of the data.

Answer 1

The value of r² would decrease substantially because this point does not follow the pattern of the data.

Step-by-step explanation:

The correct answer option is 4) The value of r² would decrease substantially because this point does not follow the pattern of the data.

When a point does not follow the pattern of the data, it is considered an outlier. Outliers can have a significant impact on the value of r², especially if they are influential points that significantly impact the slope of the line of best fit. In this case, since the point is not following the pattern of the data, its exclusion would result in a decrease in the value of r². This is because r² represents the percentage of variation in y that is explained by variation in x using the regression line, and the inclusion of an outlier can introduce more variability and reduce the overall fit of the model.