Exploring Linear Regression and Correlation Coefficient

The video tutorial introduces linear regression, explaining its use in making predictions from scatter plots. It demonstrates how to use TI-84 calculators for accurate line of best fit calculations. The correlation coefficient, denoted as 'r', is discussed, highlighting its role in measuring the strength and direction of data relationships. The tutorial provides step-by-step instructions for performing linear regression on a calculator, followed by practical examples involving graph matching, predicting alligator weight, and analyzing department store data.

What is the primary purpose of linear regression?

• To find the average of a data set

• To calculate the mode

• To determine the median value

• To find the line of best fit

Which calculator is mentioned as useful for performing linear regression?

• HP 35s

• TI-83

• TI-84

• Casio FX-991EX

What does the correlation coefficient (r) measure?

• The average of the data

• The median of the data

• The strength and direction of the relationship between two variables

• The mode of the data

What is the range of the correlation coefficient (r)?

• -2 to 2

• 0 to 1

• -0.5 to 0.5

• -1 to 1

What is the first step in finding the line of best fit using a graphing calculator?

• Entering the data

• Plotting the data

• Turning on diagnostics

• Calculating the mean

In the alligator weight example, what is the correlation coefficient (r) value?

• 0.67

• 0.995

• 0.92

• 0.27

What is the equation for the line of best fit in the alligator weight example?

• y = 0.27x + 5.82

• y = 0.67x + 2.5

• y = 0.92x + 1.5

• y = 0.995x + 3.2

In the department stores example, what is the correlation coefficient (r) value?

• -0.67

• -0.947

• 0.92

• 0.67

What is the equation for the line of best fit in the department stores example?

• y = -250.6x + 6000.2

• y = -300.5x + 7000.1

• y = -400.7x + 9000.3

• y = -375.4x + 8052.2

In what year would you expect there to be 4,000 department stores left?

• 2022

• 2030

• 2025

• 2027