This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Announcements • Midterm 2 tomorrow Monday April 19 7pm, Foellinger • Some office hours still on Monday, check Compass • Tutoring hours too... Feel free to raise questions as we go along, and we’ll have time for Q and A, or looking at old midterm problems at end... Break down Excel output Top portion: Regression Statistics Multiple R .632 R Square .400 Adjusted R Square .381 Standard Error .589 Observations 100 Top Portion of Excel output • Multiple R • Multiple R = √ R 2 • Multiple R =  r  in simple regression • To figure out sign of r using Multiple R, look at sign on b 1 or test stat on b 1 • R Square • Also: Coefficient of Determination • R 2 = cov ( x , y ) 2 s 2 x s 2 y = SSR SST = 1 SSE SST • Proportion of variation in y that is explained by the variation in the independent variables • Between 0 and 1 • Ajdusted R Square • adj. R 2 = 1 SSE / ( n k 1) SST / ( n 1) = 1 SSE * ( n 1) SST * ( n k 1) • Proportion of variation in y that is explained by the variation in the independent variables, adjusting for degrees of freedom • Always less than R 2 , unless equal to 1. Negative values definitely possible Top Portion of Excel output • Standard Error • Standard error of the estimate, s e , s ε , standard error of the regression line • s ε = q SSE n k 1 = √ MSE • Can use empirical rule to describe ‘spread’ of points around regression line • 95% of data expected to be within ± 2 * s ε around regression line • 68% of data expected to be within ± 1 * s ε around regression line • Observations (we’ll skip this ...) Break down Excel output Middle portion of output: ANOVA df SS MS F Significance F Regression k SSR MSR F test stat pvalue Residual nk1 SSE MSE Total n1 SST • SSR + SSE = SST • MSR = SSR k • MSE = SSE n k 1 • F test stat = MSR MSE • pvalue is on overall F test • Don’t confuse with oneway ANOVA formulas on Midterm 1 Middle Portion of Excel output This portion of output can obviously be used to find things like R 2 , s ε ,... But reason it is included is overall F test: H : β 1 = β 2 = ... = β k = 0 At least one β i 6 = 0 F distribution, with k and n k 1 degrees of freedom Onetailed, right hand side test So α is put entirely on the right Reject H if test stat > critical value or pvalue < α implies Model is valid Do not reject H if test stat < critical value or pvalue > α implies Model is not valid Break down Excel output Bottom portion of output: Coeff. Standard Error t Stat Pvalue Lower 95% Intercept b s b b s b 2 tail p b t ( . 025 , n k 1) s b X1 b 1 s b 1 b 1 s b 1 2 tail p b 1 t ( . 025 , n k 1) s b 1 . . . (Got rid of Upper 95% for space) So Excel always assumes we are doing a twotailed test for β i = 0 vs β i 6 = 0. Bottom portion of output So we have formulas for simple regression to find b and b 1 b 1 = cov ( x , y ) s 2 x = ∑ x i y i n ¯ x ¯ y ∑ x 2 i n (¯ x ) 2 b = ¯ y b 1 ¯ x Formulas for multiple regression  too complicated for 203.Formulas for multiple regression  too complicated for 203....
View
Full
Document
This note was uploaded on 02/14/2011 for the course ECON 203 taught by Professor Petry during the Spring '09 term at University of Illinois, Urbana Champaign.
 Spring '09
 PETRY
 Economics

Click to edit the document details