Variance Analysis: Line of Best Fit, Explained Variability, and F-Test, Slides of Economic statistics

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Review of Analysis of variance

concepts

1 2 3 4 5 6 7

total = 42

( y y )

i

− ( 4 - 5.4) 2 = 2. ( 7 - 6.3) 2 = 0. ( 6 - 7.1) 2 = 1. ( 12 - 8.0) 2 = 16. ( 8 - 8.9) 2 = 0. ( 9 - 9.7) 2 = 0. ( 10 - 10.6) 2 = 0. Total = 21.

( ˆ )

i i

y − y Variability

( y ˆ y )

i

−

What is the line that best fits the data?

• Easy, use least squares estimation. Y = 4.57 + 0.857 X

What percentage of the variability is explained by the new reference line?

• Easy!

Sometimes called R-square

42 =0.

The test

• Requires further calculations, but the

important figure is the p-value of

• How do you interpret it?

Assumptions for the interpretation of the p-value

• Errors are independently distributed
• Errors follow a normal distribution with mean 0 and constant variance
• If the assumptions are not right, the residual variance from the ANOVA will be larger than it should be and the model is not appropriate