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# Economics 105: Statistics - PowerPoint PPT Presentation

Economics 105: Statistics. GH 22 & 23 due Thursday, 17 th GH 24 (last one! Please rejoice silently. ) due Thur 24 th Unit 3 Review will be due Tuesday, 29 th (I’ll hand it out Thur 24 th ). It’ll cover what we get through.

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## PowerPoint Slideshow about 'Economics 105: Statistics' - karis

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### Economics 105: Statistics

GH 22 & 23 due Thursday, 17th

GH 24 (last one! Please rejoice silently.) due Thur 24th

Unit 3 Review will be due Tuesday, 29th (I’ll hand it out Thur 24th). It’ll cover what we get through.

I’ve decided NOT to squeeze in the individual RAP presentations. I will move that % of your grade to RAP & Review 3.

Quadratic models may be considered when the scatter diagram takes on one of the following shapes:

Y

Y

Y

Y

X1

X1

X1

X1

β1 < 0

β1 > 0

β1 < 0

β1 > 0

β2 > 0

β2 > 0

β2 < 0

β2 < 0

β1 = the coefficient of the linear term

β2 = the coefficient of the squared term

Testing the Overall Model

• Estimate the model to obtain the sample regression equation:

• The “whole model” F-test

H0: β1 = β2 = β3 = … = β15 = 0

H1: at least 1 βi ≠ 0

• F-test statistic =

Testing the Overall Model

Critical value = 2.082= F.INV(0.99,15,430-15-1)

p-value = 0 = 1-F.DIST(120.145,15,430-15-1,1)

Testing for Significance of just a Quadratic Term

• t-test

• Reports the proportion of total variation in Y explained by all X variables taken together

• Consider this model

(continued)

52.1% of the variation in pie sales is explained by the variation in price and advertising

• R2 never decreases when a new X variable is added to the model

• What is the net effect of adding a new variable?

• We lose a degree of freedom when a new X variable is added

• Did the new X variable add enough explanatory power to offset the loss of one degree of freedom?

(continued)

• Penalizes excessive use of unimportant variables

• Smaller than R2and can increase, decrease, or stay same

• Useful in comparing among models, but don’t rely too heavily on it – use theory and statistical signif

(continued)

44.2% of the variation in pie sales is explained by the variation in price and advertising, taking into account the sample size and number of independent variables

• Linear-Log

• Log-linear

• Log-log

• Log of a variable means interpretation is a percentage change in the variable

• (don’t forget Mark’s pet peeve)

• Here’s why: ln(x+x) – ln(x) =

• calculus:

• Numerically: ln(1.01) = .00995 = .01

• ln(1.10) = .0953 = .10 (sort of)

• A dummy variable is a categorical explanatory variable with two levels:

• yes or no, on or off, male or female

• coded as 0’s and 1’s

• Regression intercepts are different if the variable is significant

• Assumes equal slopes for other explanatory variables (i.e., equal marginal effects!)

• “Dummy Variable Trap”

• If more than two categories, the number of dummy variables included is (number of categories - 1)

Dummy Variable Example (with 2 categories)

• E[ GPA | EconMajor = 1] = ?

• E[ GPA | EconMajor = 0] = ?

• Take the difference to interpret EconMajor

Dummy Variable Example (More than 2 categories)

• Model the effect of class year on GPA, controlling for study hours