When you determine if there is an association between two variables, it is also important for...

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

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

2365

Mercedes/Benz SLK

3020

Mitsubishi Eclipse

3235

Pontiac Firebird

3545

Porsche Boxster

2905

Saturn SC

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?

Solutions

Expert Solution

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.

orchestra answered 1 year ago

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