Question

use the given data to find the equation of the regression line. examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
x 11 9 13 10 10 13 7 4 11 8 5
y 7.81 6.44 12.67 7.4 7.61 8.89 5.8 5.44 8.03 6.23 5.92
create a scatterplot of the data. choose the correct graph below.
a.
b.
c.
d.

Explanation:

Step1: Analyze x and y values

First, list out the x and y pairs: (11,7.81), (9,6.44), (13,12.67), (10,7.4), (10,7.61), (13,8.89), (7,5.8), (4,5.44), (11,8.03), (8,6.23), (5,5.92). Notice that when x is 13, there are two y - values (12.67 and 8.89), when x is 10, two y - values (7.4 and 7.61), and when x is 11, two y - values (7.81 and 8.03). Also, the x - values range from 4 to 13, and y - values from ~5.44 to 12.67.

Step2: Compare with graphs

• Graph A: Has a point around x = 15, y = 13 - 14, which matches the (13,12.67) point. Also, the other points cluster around lower x and y, with the two - x (10,11,13) having multiple y - points.
• Graph B: The points seem to have a different distribution, with a more linear trend in the lower x, but the multiple y - points for same x are not as clear.
• Graph C: The point at x = 15 is not as high as 12.67, and the clustering is different.
• Graph D: The point at x = 15 is not as high as 12.67, and the spread of y - values for same x is not captured.

Looking at the data, when x = 13, y = 12.67 is a relatively high point. Graph A has a point in the upper range (around x = 15, y = 13) which corresponds to (13,12.67) (since x = 13 is close to x = 15 in the graph's scale). Also, the multiple points for x = 10,11,13 (with different y - values) are represented in Graph A with the cluster and the high - y point.

Answer:

A. The graph labeled A