Question

Five observations taken for two variables follow.
xi 4 6 11 3 16
yi 50 50 40 60 30
​a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship
between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.

Answer 1

Answer:

-60 ; -0.9689

Step-by-step explanation:

Given the data:

xi 4 6 11 3 16

yi 50 50 40 60 30

The scatter diagram indicates a linear negative relationship between x and y. Thia is indicated by the negative direction of the trend line.

Sample covariance formula:

Σ(x-xi)(y-yi) / n - 1

Using calculator : sample covariance = - 60

The variables have negative covariance meaning an increase in one variable leads to a corresponding decrease in the other.

Sample correlation Coefficient : -0.9689

This shows that a very strong negative correlation exists between both variables. Because the correlation coefficient value is very close to - 1.