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
Unlock Document

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

Log In


OR

Join OneClass

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

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit