Algebra 2 Warm up 5.4.13

Write a brief description of how to determine each statistical measure:a. Meanb. Variancec. Ranged. Mediane. Standard Deviationf. Mode

Correlation

• Correlation is relationship between 2 variables.– Example: There is a positive relationship between

the type of house you live in and the amount of money you make. The more money you make the nicer you house you probably have.

• The idea is to plot out the data and see if they all align up together on one curve.

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Y

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Y

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Linear relationships Curvilinear relationships

Various Correlations

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Correlation Coefficient , (r)

A number between –1 and 1, used to describe the “correlation” between 2 data points. 0 = No relationship between the data. –1 = A strong negative linear relationship 1 = A strong the positive linear relationship

The more closely aligned data is, the higher the correlation .

Scatter Plots of Data with Various Correlation Coefficients

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r = -1 r = -.6 r = 0

r = +.3r = +1

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Xr = 0

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Y

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Y

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Y

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Strong relationships Weak relationships

Linear Correlation

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Linear Correlation

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No relationship

Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

Example• A director of sales for Blockbuster Video wants to predict

future sales of his videos• He believes that there is a correlation between the number

of sales he will make and the number of houses that have a VCR.

• He compiles some data and makes a chart:

Example• Treating the data as ordered pairs he makes a “scatter plot” of

the data:

Example• There appears to be a “linear” relationship between the data.• They all line up pretty nicely to a straight line.• The data has a HIGH positive correlation

But what is the correlation coefficient?

• There is a nasty formula we could use to find it that looks like this:

• We won’t be using that (Thankfully)• We will be using Technology!

Regression line

• An equation that best describes the data. • Remember an equation of a line gives you

each point, so we can use this to predict!• From the technology we got:

y = 2.81 x - 15.12

X = households with VCRS ( in millions)Y = Sales

Homework

1. Think about 2 things that might be correlated.2. Create a hypothesis (or a prediction)3. Poll at a minimum 10 people.4. Record your data in a Google spreadsheet

Remember there needs to be 2 columns5. We will test your hypothesis tomorrow. Example:

• Will the number of students who are absent vary according to the temperature?

• Does the color of one’s car correlate to their income?• Will music help students study and if so what kind?