Question

Born to be old? Is there a relationship between the gestational period (time from conception to birth) of an animal and its average life span? The figure shows a scatterplot of the gestational period and average life span for 43 species of animals.

a. Describe the relationship shown in the scatterplot.

b. Point A is the hippopotamus. What effect does this point have on the correlation, the equation of the least-squares regression line, and the standard deviation of the residuals?

c. Point B is the Asian elephant. What effect does this point have on the correlation, the equation of the least-squares regression line, and the standard deviation of the residuals?

Short answer

Part (a) Direction: Positive.

Form: Curved.

Strength: Moderately strong.

Part (b) Point $A$ lowers the correlation, increases the $y-$intercept but not the slope, and lowers the standard deviation of the residuals.

Part (c) Point $B$ raises the correlation while leaving the regression line and standard deviation unchanged.

Step-by-step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

Thus, from the scatterplot we can say that:

Direction: Because the scatterplot slopes upwards, it is positive.

Form: Because there is curvature in the data, it is curved.

Strength: Because the points are not too far apart, but not too close together, they are moderately strong.

Part (b) Step 1: Explanation

The hippopotamus is at point $A$

As a result, Point $A$ lowers the correlation because it looks to be an outlier, skewing the data and lowering the correlation of the data set. Point $A$ will increase the $y-$intercept but have little effect on the slope. Point $A$ will have little effect on the slope because it is near to $x$ but far from $y$ It will, however, increase the $y-$intercept for the same reason. The standard deviation of the residuals is increased by point $A$ This is due to the huge residue at point A.

Part (c) Step 1: Explanation

An Asian elephant is Point $B$

As a result, point $B$ is in the pattern's extension in the majority of the points in the scatterplot, and as a result, point $B$ is roughly near the regression line, increasing the correlation. Furthermore, it will have no effect on the regression line. Point $B$has little effect on the standard deviation because the observed $y-$values are about the same as the expected value.