Question

the point circled on the scatterplot is considered an influential point. a new least-squares regression line will be calculated with the influential point removed. how will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?

Answer 1

Removing an influential point from a scatterplot can significantly affect the new least-squares regression line for the remaining points.

Step-by-step explanation:

An influential point in a scatterplot is an observed data point that is far from the other data points in the horizontal direction. When removing an influential point from a scatterplot, a new least-squares regression line is calculated for the remaining points. The removal of the influential point can have a significant effect on the new least-squares regression line for the remaining points.

To determine the impact of the influential point on the new regression line, you can compare the slope and correlation coefficient of the original regression line to the slope and correlation coefficient of the new regression line. If the influential point has a significant effect, the slope and correlation coefficient of the new regression line will be different from the original values.

For example, if the influential point is an outlier that is far from the other data points, its removal can result in a regression line that fits the remaining data more closely, with a different slope and correlation coefficient.

Answer 2

Removing the influential point will alter both the slope and y-intercept of the new least-squares regression line for the remaining 14 points in unpredictable ways.

Step-by-step explanation:

Influential points significantly distort the data distribution, impacting the line that best fits the remaining points. Removing such a point has several consequences:

Slope: The influential point likely pulled the line towards itself, making the slope steeper or less steep depending on its location. Removing it might change the slope's magnitude or even its sign (positive to negative or vice versa) if the remaining points suggest a different trend.

Y-intercept: If the influential point was far from the other points horizontally, it likely shifted the line vertically to "catch" it. Removing it might shift the line back, potentially increasing or decreasing the y-intercept depending on the remaining points' distribution.

Therefore, the removal's specific effects depend on the influential point's location and the remaining data distribution. Both the slope and y-intercept are likely to change.

In summary, the removal of an influential point significantly impacts the new regression line, making Option A (y-intercept remains same) and Option B (y-intercept decreases and slope negative) unlikely scenarios.

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Complete Question

The point circled on the scatterplot is considered an influential point. a new least-squares regression line will be calculated with the influential point removed. how will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?

A. The y-intercept will remain the same, and the slop will be negative.

B. The y-intercept will decrease, and the slop will be negative.

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The missing scatterplot is attached.