Economics 105 statistics
Download
1 / 33

Economics 105: Statistics - PowerPoint PPT Presentation


  • 77 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Economics 105: Statistics' - karis


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Economics 105 statistics

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 regression model
Quadratic Regression Model

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
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 model1
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
Testing for Significance of just a Quadratic Term

  • t-test



Coefficient of determination for multiple regression
Coefficient of Determination for Multiple Regression

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

  • Consider this model


Multiple coefficient of determination
Multiple Coefficient of Determination

(continued)

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


Adjusted r 2
Adjusted R2

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

    • disadvantage when comparing models

  • 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?


Adjusted r 21
Adjusted R2

(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


Adjusted r 22
Adjusted R2

(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


Log functional forms
Log Functional Forms

  • 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)


Log functional forms1
Log Functional Forms

  • Here’s why: ln(x+x) – ln(x) =

  • calculus:

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

  • ln(1.10) = .0953 = .10 (sort of)












Dummy variables
Dummy Variables

  • 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
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
Dummy Variable Example (More than 2 categories)

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


ad