Chapter 3, Problem T3.12SPT

(a)

To determine

To identify the unusual point in the scatterplot and estimate its x and y coordinates.

Answer to Problem T3.12SPT

  $(-19.4,340)$ .

Explanation of Solution

The unusual point is the point that deviates from the general pattern in the other points which is the point in the top right corner of the scatterplot. We note that this point corresponds approximately with $-19.4$ on the horizontal axis and $340$ on the vertical axis which implies that the coordinates of the point are approximately $(-19.4,340)$ .

(b)

To determine

To describe the effect this point has on the correlation, the slope and y -intercept of the least squares line and the standard deviation of the residuals.

Answer to Problem T3.12SPT

1. Correlation decreases.
2. Slope increases and y intercept increases.
3. Standard deviation increases.

Explanation of Solution

The unusual point is the point that deviates from the general pattern in the other points which is the point in the top right corner of the scatterplot.

1. Since the unusual point deviates from the general linear pattern in the other points and the correlation measures the strength of the linear association between the variables thus the unusual point decreases the correlation.
2. Since the point lie above the regression line to the right we expect this point to make the regression line steeper and thus the slope will then increase while the y -intercept increase as well.
3. The unusual point lies furthest from the regression line, which implies that the unusual point will have the largest residual. Thus the variations in the residuals will then increase when the unusual point is included and thus the standard deviations of the residuals increases.