Assessing the Appropriateness of a Linear Correlation Model

This lesson covers how to assess the appropriateness of a linear correlation model by checking three conditions: ensuring variables are quantitative, the scatterplot looks linear, and there are no outliers. The correlation coefficient is explained, highlighting its role in determining the strength of a linear relationship. Examples, including Monopoly property costs and fuel efficiency, illustrate these concepts. Nonlinear patterns and residuals are discussed, emphasizing the importance of choosing the right model. The lesson concludes with handling outliers and a final example involving used car prices.

What does a correlation coefficient close to 0 indicate about the relationship between two variables?

• Strong positive correlation

• No correlation

• Weak linear correlation

• Strong negative correlation

Which of the following is NOT a condition for using a linear correlation model?

• The scatterplot should appear linear

• The variables must be categorical

• Both variables must be quantitative

• There should be no significant outliers

In the Monopoly property example, why was it appropriate to calculate the correlation coefficient?

• The variables were categorical

• The scatterplot showed a linear pattern

• The correlation coefficient was negative

• There were significant outliers

Why should the month number not be used as a variable in the small business sales data example?

• It is a quantitative variable

• It has significant outliers

• It is a categorical variable

• It shows a strong linear pattern

What does a clear pattern in the residual plot suggest about the data?

• The data is perfectly linear

• A nonlinear model might be more appropriate

• There are no outliers

• The correlation coefficient is zero

In the SAT Math Scores versus GPA example, what should be done with the outlier?

• Ignore it and proceed with calculations

• Investigate and possibly remove it

• Assume it is an error and correct it

• Use it to calculate a new correlation coefficient

What does it mean if residuals are scattered around the horizontal line in a residual plot?

• The linear model is appropriate

• The data is not linear

• The correlation coefficient is negative

• There are significant outliers