Question

Use the given data to complete parts​ (a) and​ (b) below.

x y 2.1 4 3.8 1.4 3 3.6 4.8 4.9 ​(a) Draw a scatter diagram of the data.

Choose the correct answer below.

A. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3.8); (3.6, 3); (4, 2.2); (5, 4.8). From left to right, the points have no visibly apparent upward or downward trend.

B. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). From left to right, the points have no visibly apparent upward or downward trend.

C. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (2.2, 5); (3, 1.4); (3.8, 3.6); (4.8, 4). From left to right, the points have no visibly apparent upward or downward trend.

D. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3); (3.6, 3.8); (4, 4.8); (5, 2.1). From left to right, the points have no visibly apparent upward or downward trend.

Compute the linear correlation coefficient. The linear correlation coefficient for the four pieces of data is nothing. ​(Round to three decimal places as​ needed.)

​(b) Draw a scatter diagram of the data with the additional data point left parenthesis 10.3 comma 9.4 right parenthesis.

Choose the correct answer below.

A. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). One additional point is plotted significantly above and to the right of the rest, approximately at (10.4, 9.4).

B. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (1.4, 3.8); (3.6, 3); (4, 2.2); (5, 4.8). One additional point is plotted significantly above and to the right of the rest, approximately at (9.4, 10.4).

C. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (1.4, 4.8); (3.6, 3); (5, 3.8); (9.4, 2.1). One additional point is plotted significantly above the rest, approximately at (4, 10.3).

D. 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (3, 3.6); (3.8, 5); (4.8, 1.4); (10.4, 4). One additional point is plotted significantly above and to the left of the rest, approximately at (2.2, 9.4).

Compute the linear correlation coefficient with the additional data point. The linear correlation coefficient for the five pieces of data is nothing. ​(Round to three decimal places as​ needed.) Comment on the effect the additional data point has on the linear correlation coefficient.

A. The additional data point strengthens the appearance of a linear association between the data points.

B. The additional data point does not affect the linear correlation coefficient.

C. The additional data point weakens the appearance of a linear association between the data points.

Explain why correlations should always be reported with scatter diagrams.

A. The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.

B. The scatter diagram is needed to determine if the correlation is positive or negative.

C. The scatter diagram can be used to distinguish between association and causation.

Click to select your answer(s).

Answer 1

Part A

From the scatterplot of 4 data points

B. 0 2 4 6 0 2 4 6 x y A scatter diagram has a horizontal x-axis labeled from 0 to 6 in increments of 1 and a vertical y-axis labeled from 0 to 6 in increments of 1. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). From left to right, the points have no visibly apparent upward or downward trend.

The linear correlation coefficient of four data points is 0.652

Part B

With the additional data point scatter plot,

A). 0 4 8 12 0 4 8 12 x y A scatter diagram has a horizontal x-axis labeled from 0 to 12 in increments of 2 and a vertical y-axis labeled from 0 to 12 in increments of 2. The following 4 approximate points are plotted, listed here from left to right: (2.2, 4); (3, 3.6); (3.8, 1.4); (4.8, 5). One additional point is plotted significantly above and to the right of the rest, approximately at (10.4, 9.4).

Correlation coefficient with additional data point is 0.939

The effect the additional data point has on the linear correlation coefficient is A. The additional data point strengthens the appearance of a linear association between the data points.

Correlations should always be reported with scatter diagrams because A) The scatter diagram is needed to see if the correlation coefficient is being affected by the presence of outliers.