A recent newspaper article reported that the number of personal computers being sold is increasing. In addition, the number of athletic shoes being sold.

*What is the Correlation?

A recent newspaper article reported that the number of personal computers being

sold is increasing. In addition, the number of

athletic shoes being sold is also increasing. They report

that there is a strong correlation between these

two events? What do you think?

*What is a Correlation?

*A relationship between two variables that are being measured.

Negative Correlation

- the value of one variable will increase

and the other will decrease

Positive Correlation

-the value of both

variables increases

No Correlation

-no apparent

relationship between

the variables increasing

or decreasing

*Order Card Set #1 on your Desk based on the Direction of the Correlation.

*(Negative to Positive)

*What order did you place the cards in?

*Did you have any difficulty with this task?

*Strength of a Correlation?

*You can further classify a correlation by determining if it is a strong or weak correlation.

Perfect Negative Correlatio

n

Perfection Positive

Correlation

No Correlation

StrongNegative

WeakNegative

StrongPositive

WeakPositive

*Order Card Set #2 on your Desk based on the Strength and Direction of the Correlation.

*Negative to Positive

*How sure are you that you have the cards in the correct order?

*Correlation using Scatter Plots*If you have actual collected data for a

situation, you can use a scatter plot to determine the correlation of the variables that are being compared.

*Attach the data charts and scatter plot graphs from Card Set #3 to the situations from Card Set #2. Then look at the scatter plots and reorder your cards if needed.

*Negative to Positive

*How sure are you that you have the cards in the correct order?

*How did you use the scatter plots to change the position of a card, or to confirm that you had it in the correct spot?

*Are any of the situations still hard to decide where they fit in relation to the correlations of the other situations?

Does adding a line of best fit help determine the correlation of two events?

Would finding the equation of the line of best fit help us determine anything about the correlation?

*Add the line of best fit to each of the scatter plots on your cards and calculate the equation for the line of best fit. Then reorder the cards if needed.

*Negative to Positive

*To get the equation of a line:

*1 – pick two points that the line passes through and calculate the slope using the slope formula

*2 – Use the slope an one point in the point slope form

*3 – Change the equation to slope intercept form

*What do you notice about the slope of the line of best fits that you found and the correlation that you have chosen for each situation?

*What problems could arise from relying on the line of best fit to determine the correlation?

*Correlation Coefficient*Defined as a numerical representation of the

strength and direction of the relationship between two variables/events.

*It measures the amount of variance that you have in your data

*It is a number between -1 and 1 that represents how similar the two variables/events are.

*The closer a the number is to 1 or -1, the stronger the correlation. The closer the number is to 0, the weaker the correlation.

-1

Perfect Negative Correlatio

n

+1

Perfection Positive

Correlation

0

No Correlation

StrongNegative

WeakNegative

StrongPositive

WeakPositive

-0.82

Strong Negative Correlation

0.3 Weak Positive Correlation

0.7 Strong Positive Correlation0 No Correlation

-0.04

Weak Negative Correlation1.2 Not a correlation #

*Calculate

*There are two ways to find the correlation coefficient

*By hand using the formula:

*Using Technology, we can calculate the correlation coefficient using several different methods.

*Using Microsoft Excel Spreadsheets

*Using Graphing Calculators

*Graphing Calculator using Linear Regression

*Be sure that your Diagnostics is turned on

*On newer calculators

*Select MODE

*Scroll Down to bottom of screen to STAT DIAGNOSTICS and select on

*Example

What is the correlation of temperature and ice cream sales?

How strong is the correlation?

*Example*Create the x/y table on your calculator

*Select STAT on calculator

*Under EDIT tab, select 1:Edit…

*Enter all x values (temperature) under

*Enter all y values (ice cream sales) under

*Calculate the Linear Regression of your data

*Select STAT on calculator

*Under CALC tab, select 1:LinReg(ax+b)

*Xlist: and Ylist: or LinReg(ax+b)

*a and b are used to get line of best fit in the form of

*r is the correlation coefficient

*Example

Line of Best Fit:

Correlation Coefficient:

Strong Positive Correlation

*Using your situation cards from yesterday, input the data into your graphing calculator and use the Linear Regression Feature on to:

*Calculate the actual Line of Best Fit

*Find the Correlation Coefficient

*Reorder the Cards *Negative to Positive

A recent newspaper article reported that the number of personal computers being

sold is increasing. In addition, the number of

athletic shoes being sold is also increasing. They report

that there is a strong correlation between these

two events?

What would be the best way to determine the answer to

this question?

*Comparing More Variables*Our school wants to start offering

nutritional cereal for breakfast. They ask you to look at the nutritional rating of different cereal brands and decide which ones we should offer.

*They recommend that you start by looking at the correlation of the nutritional rating to each of three variables: fat, sugar, and protein.

*What do you think that you can determine by looking at these correlations?

*Sugar and Fat have Negative Correlation with Nutritional Rating

*Protein has Positive Correlation with Nutritional Rating

*Need Correlation Coefficient to determine which one has the strongest correlation

*We CANNOT state that any of theses factors causes the high nutritional rating!