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Chapter 10: Q. 23 (page 670)

A scatterplot and a least-squares regression line are shown in the figure below. If the labeled point P(20,24)is removed from the data set, which of the following statements is true ?

(a) The slope will decrease, and the correlation will decrease.

(b) The slope will decrease, and the correlation will increase.

(c) The slope will increase, and the correlation will increase.

(d) The slope will increase, and the correlation will decrease.

(e) No conclusion can be drawn since the other coordinates are unknown.

Short Answer

Expert verified

Option (b) ,The slope will decrease and the correlation will increase.

Step by step solution

01

Given information

We are given a scatterplot and a point P(20,24)

We are asked what will be effect on correlation and slope of line if point Pis removed.

02

Explanation

We have an upward sloping regression line it means 0<r<1

We know ris not going to be equal 0as for this situation line would go perfectly through all of dots and it's clear that point right over here is indeed an outliner. The residual between point Pand line is quite high, so it would be negative residual.

On removing point Pvalue of correlation(r)will increase as we are removing point that was having negative residual.

And slope of line will decrease as line will move slightly clockwise due to removal of point P.

Hence, option localid="1650437721622" (b)is correct as it satisfies our explanation.

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