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.

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 $P$is removed.

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

We know $r$is not going to be equal $0$as 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 $P$and line is quite high, so it would be negative residual.

On removing point $P$value of correlation$\left(r\right)$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" $\left(b\right)$is correct as it satisfies our explanation.