Q. 4.151 - Elementary Statistics

Question

Consider the following set of data points 

x	-3	-2	-1	0	1	2	3
y	9	4	1	0	1	4	9

a. Compute the linear correlation coefficient, r.

b. Can you conclude from your answer in part (a) that the variables x and y are unrelated? Explain your answer.

c. Draw a scatterplot for the data.

d. Is use of the linear correlation coefficient as a descriptive measure for the data appropriate? Explain your answer.

e. Show that the data are related by the quadratic equation y = x². Graph that equation and the data points.

Step-by-Step Solution

Answer

The solution graph is 

Step 1. Given

x	-3	-2	-1	0	1	2	3
y	9	4	1	0	1	4	9

Step 2. Find the linear coefficient using MINTAB

1 Save x & y data on the given problem.

2 Select Statistics- Basic Statistics - Relationships ....

3 Specify the x & y in the Flexible text box.

4 Click OK.

Step 3. Determine the correlation coefficient

Step 4. Solution b

b) We cannot conclude that the variables x and y are not related. There is no linear relationship between these two variables.

Step 5. Using Minitab we draw a scatter plot

Step 6. Solution d

The use of the linear coefficient as a descriptive measure of data is inappropriate. Because the data points don't seem to be scattered about the line.

Step 7. The graph of equation