Question

When you determine if there is an association between two variables, it is also important for you to determine how strong or weak that association is. This is why, when you have data for two quantitative variables, you calculate what is called the coefficient for correlation.

Instructions

1. Suppose you are determining the association between the weight of a car and the miles per gallon that the car gets. Answer the following questions in a Word document:

• define correlation and explain how you can use correlation to determine the relationship between these two variables.
• Before you look at some data, what kind of association do you think will exist between the weight of a car and the miles per gallon that the car gets? Will it be positive or negative?
• Given the data below, use Excel or other technology to calculate the correlation coefficient for this data:

Model

City MPG

Weight

Mazda MX-5 Miata

25

2365

Mercedes/Benz SLK

22

3020

Mitsubishi Eclipse

23

3235

Pontiac Firebird

18

3545

Porsche Boxster

19

2905

Saturn SC

27

2420

• Now that you have calculated the correlation, what does this value represent? What does it tell you about the relationship between these two variables?

Answer 1

a) Define correlation and explain how you can use correlation to determine the relationship between these two variables.

Ans: In a bivariate distribution we may be interested to find out if there is any correlation or covariation between the two variables under study. If the change in one variable affects a change in the other variable, the variables are said to be correlated.

b) Before you look at some data, what kind of association do you think will exist between the weight of a car and the miles per gallon that the car gets? Will it be positive or negative?

Ans: Before we look at some data, we would think the kind of association exist between the weight of a car and the miles per gallon that the car gets will be increased the value of the weight of a car when the value of the miles per gallon that the car gets will be decreased. It will be negative.

c) Given the data below, use Excel or other technology to calculate the correlation coefficient for this data:

Ans: The correlation coefficient for this data is -0.7945.

The correlation value -0.7945 represent the strength of the association between the weight of a car and the miles per gallon. It tells us about the strong negative relationship between these two variables.