Correlation and Regression Analysis Concepts

This lesson teaches how to assess the appropriateness of a linear correlation model by checking three conditions: quantitative variables, linear appearance of scatter plots, and absence of outliers. Examples include Monopoly property costs, monthly sales data, fuel efficiency vs. speed, SAT scores vs. GPA, and used car prices. The lesson emphasizes the importance of examining datasets for patterns and considering nonlinear models when appropriate.

What does a correlation coefficient close to zero indicate?

• Weak linear correlation

• Strong negative correlation

• No correlation

• Strong positive correlation

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

• No significant outliers

• Data must have outliers

• Scatter plot must look linear

• Variables must be quantitative

In the example of monopoly property costs, what was the correlation coefficient?

• 0.5

• 0.7

• 0.9

• 1.0

Why should we not proceed with a correlation coefficient calculation for the sales data example?

• One variable is categorical

• The data is not linear

• The correlation coefficient is too high

• There are outliers

What does a pattern in the residuals suggest about the data?

• There are no outliers

• The correlation coefficient is zero

• A nonlinear model might be more appropriate

• The data is perfectly linear

In the fuel efficiency versus speed example, what shape did the residual plot form?

• A parabola

• A straight line

• A zigzag pattern

• A circle

What should be done when an outlier is found in a dataset?

• Always remove it

• Assume it's an error

• Ignore it

• Investigate the reason for deviation

In the SAT scores versus GPA example, what was the suspected reason for the outlier?

• Student's illness

• Incorrect test score

• Data entry error

• High test anxiety

What is the relationship between used car prices and mileage?

• Positive correlation

• Negative correlation

• No correlation

• Perfect correlation

What is the purpose of plotting residuals?

• To find the correlation coefficient

• To confirm linearity

• To calculate averages

• To identify patterns not visible in the scatter plot