Study Guides (248,404)
United States (123,353)
Boston College (3,492)
Economics (366)
ECON 1151 (14)
All (14)

# COMPLETE Statistics Notes - Part 6 (got 4.0 in the course)

4 Pages
77 Views

School
Department
Economics
Course
ECON 1151
Professor
All Professors
Semester
Spring

Description
Final—Regressions Keely Henesey Simple Regression Model Population Regression Model Population Model yi=β 0β x1+εi i y iβ +0 x 1β1x +…2ε2 i i i Observed Value yi=b 0b x1+i i y ib +0 x 1b1i …2e i i y =b +b x yi=b 0b x1+b1x …2 2 i 0 1 i i Cov(x,y) sy ∑ (xi−́x)( í y ) ∑ (xi−x́) Predicted Value b1= 2 =r = 2 = yi sx sx ∑ (xi−x́) ∑ (xi−́x)x i b =́ y−b ́ x 0 1 ei=Observed−Predicted= y −̂ i yi=y i b(+0 x 1 i Residual e → ModelError+Sample Error b ,b ,b ,… i ( 0 1 2 ) SST=SSR+SSE (y −́ y) (̂y −́y) (y −̂ y ) Sum of Squares Total i i i i 2 2 SST= ∑ (yi−́y )(n−1)s y 2 2 2 2 2 Sum of Squares Regression SSR= ∑ (yi−́y )b 1∑ (xi−x́)=b (1−1)s x 2 ̂ 2 ( ) 2 2 2 ( ) 2 SSE= ∑ ei= ∑ (y iy =in−1 s −b ( y n−K1 x) e Sum of Squares Error SSE= y − b +b x = y − ́y+b x −́ x 2 ∑ ( i ( 0 1 i) ∑ [ i ( 1( i )] SST Mean Square Total MST= n−1 SSR Mean Square Regression MSR= K Mean Square Error MSE=σ =s = 2 SSE e (n−K−1 ) SSR SSE Coefficient of Determination R = =1− SST SST *Stops irrelevant independent variables from causing some small reduction in the  SSE (provides better comparison between multiple regression models with varying  numbers of independent variables) Adjusted Coefficient of  Determination 2 ́ 2 SSE/ n−K−1 ) MSE se R =1− SST / n−1 ) =1− MST =1− MST 2 2 Coefficient of Correlation r= √ R=r(̂ y, y)= √ Final—Regressions Keely Henesey Sampling Distribution of Least Squares Coefficient Estimator Simple Regression Model Population Regression Model Mean E [ ]1 1 2 2 2 σ 2 σ2 2 s e se σb1 2= 2 sb1 = 2 ∑ (xi−x ́) (n−1)s x (n−1)s 1−x( x x ) ( 1−r x x)∑ (x1−́ x ) 1 1 2 1 2 i Variance 2 se se 2 s2e se sb= = sb2 = 2 1 ∑ (xi−x́ ) (n−1)s x (n−1)s 1−x( x x ) ( 1−r x x)∑ (x2−́ x ) 2 1 2 1 2 i How to Decrease  Increase  n  or  s 2 ; Decrease  2  or  r2 Variance xi se x1x2 If Conditions Hold… − Regression Errors  ε  are Normally Distributed i Student’s  t   b Approximation − Standard Least Squares Assumptions Hold (or distribution of  1 is approximately normal) b jβ j tn−K−1 =t bj sbj Tests of Population Regression Slope  β 1 Null Hypothesis ( Alternative Hypothesis ( Reject  H  if… p­Value H 0 ) H 1 ) 0 ¿ H 0β =βj j ¿
More Less

Related notes for ECON 1151
Me

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.