Scatterplots and Line of Best Fit Correlation

Scatterplots, Correlation Coefficients, & Line of Best Fit

Algebra 1

Example

A group of scientists were conducting a study on a particular type of crime in Lexington, Kentucky. They conducted the study over 10 years and the results are shown in the table below, where x represents the year and y represents the number of times that crime was committed.

Use Desmos to construct a scatterplot of the given data.

Example Answers

A) What is the equation for the line of best fit?  y=-3.93939x+55.4667

B) What is the correlation coefficient, r?  r=-0.9857

  

C) What does the correlation coefficient tell you about the number of years passing and the number of crimes being committed in the area?  There is a strong negative correlation. As time passes, less crimes are being committed.

  

D) Use the line of best fit to determine the number of crimes that will be committed in the 12th year of the study.

y=−3.93939(12)+55.4667 

y≈8

  

You Try It #1

The profit of a company is based on the price of the product it sells. The table below shows how the profit of a company (y) is related to the cost of one of its products (x).

Open Ended

 A) What is the line of best fit?

Multiple Choice

 B) What is the correlation coefficient, r? (Round to the nearest hundreth.)

• $$r=0.5$$  

• $$r=-0.67$$  

• $$r=-0.32$$  

Multiple Choice

C) What does the correlation coefficient tell you about the cost of the product & the profit? 

• Strong Negative Correlation

• Weak Negative Correlation

• No Correlation

• Weak Positive Correlation

• Strong Positive Correlation

Multiple Choice

D) Use the line of best fit to determine the profit in thousands if the cost of the product was $15. (Round to the nearest tenth.)

• $$y=-49.9$$  

• $$y=49.9$$  

• $$y=-0.5$$  

• $$y=5.8$$  

You Try It #2

The table shows the IQ of 7 senior students (y) along with the number of hours of TV each student views per week (x).

Open Ended

 A) What is the line of best fit?

Multiple Choice

 B) What is the correlation coefficient, r? (Round to the nearest hundreth.)

• $$r=-0.95$$  

• $$r=-0.66$$  

• $$r=0.24$$  

Multiple Choice

C) What does the correlation coefficient tell you about the number of hours each student is watching TV per week and their IQ?

• Strong Negative Correlation

• Weak Negative Correlation

• No Correlation

• Weak Positive Correlation

• Strong Positive Correlation

Multiple Choice

D) Use the line of best fit to determine the approximate IQ of a student who spends about 2 hours watching TV per week.

• $$y\approx124$$  

• $$y\approx108$$  

• $$y\approx47$$