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Statistics I

Lesson 20

Regression cont.

16th April 2010

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Today

Interpretation of the Regression Coefficients

How good is your regression model? (Coefficient ofDetermination)

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Back to Armands Pizza Parlour

Interpretation of Coefficients

Effect of Student Population Size on

Quarterly Sales for Armand's Pizza

Parlours

y = 60 + 5x

0

50

100

150

200

250

0 5 10 15 20 25 30

Student Population (000s)

Qua

rterlySales(000s)

Intercept: 60 what doesthis mean?

Slope: 5 what does

this mean?

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Interpretation of Regression Coefficients

What about for the Swimmers example?

And for the Salespeople?

0 1y b b x

0 1

y b b x

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Model vs Estimated Simple Linear RegressionEquation

The estimated simple linear regression equation

0 1

y b b x

y =b0 +b1x +e

The regression model.

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So how good is your Regression Model?

Coefficient of Determination

Relationship Among SST, SSR, SSE

where:

SST = total sum of squaresSSR = sum of squares due to regression

SSE = sum of squares due to error

SST = SSR + SSE

2( )iy y2

( )iy y 2

( )i iy y

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Sums of Squares Diagram

How much ofthe totalvariationfrom theaverage

(SST) isexplainedby ourregressionmodel

(SSR) iewhat is theproportionSSR/SST?

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The coefficient of determination is:

Coefficient of Determination

where:

SSR = sum of squares due to regressionSST = total sum of squares

r2 = SSR/SST

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Coefficient of Determination for Armand

r2 = SSR/SST = 14200/15730 = .9027

The regression relationship is very strong;

90.27% of the variability in sales can be

explained by the linear relationship betweenthe size of the student population and sales.

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Sample Correlation Coefficient

2

1 )of(sign rbrxy

ionDeterminatoftCoefficien)of(sign 1brxy

where:b1 = the slope of the estimated regression

equation xbby 10

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2

1 )of(sign rbrxy

Armands Sample Correlation Coefficient

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Over to you

Now try the example questions