Math 1 December 2nd

Math 1 December 2nd

Scatter Plots, Line of "Best Fit" & Correlation Coefficient

The Alligator Project

Alligator measurements

You have been working on a science project for 8 months. Each month, you have measured the length of a baby alligator. Using your data you are trying to create a way to predict the length of the alligator at any given month.

First, is it a linear equation...

You need to find the slope of the table, if the slope is constant throughout then it is linear and you would create an equation using

 $y=mx+b$  . If it is not linear and then also not geometric you would use the process for a "line of best fit."

Measuring correlation coefficients

• The correlation coefficient, r, measures how strong correlation is. The closer r is to 1, the stronger the positive correlation; the closer it is to -1, the stronger the negative correlation. A value of r close to 0 shows relatively no correlation. 

• Correlation is another word for relationship; correlation coefficient measures the strength of the relationship.

• A correlation coefficient of 1 or -1 means that the line is linear or perfectly straight.

If you do NOT have a graphing calculator.

• If you do not have a graphing calculator you will have to use DESMOS in the meantime in order to be able to create a "line of best fit."

• On your EOC you will not have access to DESMOS and you will be required to use a graphing calculator.

• This demonstration is the SAME process for anything to do with lines of "best fit."

If you do have a graphing calculator

• This demonstration is the same process for all lines of "best fit."

• There is an error, I wrote 29 for month 7 instead of 29.5 which changed my correlation coefficient from 0.996 to 0.994

• The correct answer for the alligator problem is 0.996

• The process of finding the correlation coefficient from the calculator is entirely correct.

Fill in the Blanks

Study time vs. Test Score

• The correlation coefficient is 0.828. This is considered a strong positive correlation or relationship.

• Based on the table and the correlation coefficient we can say that there is a strong positive relationship between the amount of time you study and the score you will recieve on a test.

• We can make a prediction that says the more you study the better you will do.

Fill in the Blanks

Age of a car vs. Value of the car

• The correlation coefficient is -0.991. This is considered a strong negative correlation or relationship.

• Based on the table and the correlation coefficient we can say that there is a strong negative relationship between the age of a car and the value of the car. o

• We can make a prediction that says the older a car is the less money it will be worth.

Fill in the Blanks

Age of a music festival vs. number of attendees

• The correlation coefficient is 0.969. This is considered a strong positive correlation or relationship.

• Based on the table and the correlation coefficient we can say that there is a strong positive relationship between the age of a music festival and the number of attendees

• We can make a prediction that says the more years a music festival happens the more attendees it will recieve.

Fill in the Blanks

Price of admission vs. yearly attendance

• The correlation coefficient is -0.722. This is considered a strong negative correlation or relationship.

• Based on the table and the correlation coefficient we can say that there is a strong negative relationship between the price of admission and the number of attendees

• We can make a prediction that says the more price of admission costs the less number of people will attend.