Linear Regression

Question 1

Formula

Answer 1

y (dependent variable) = Intercept + slope x X + error

Question 2

Intercept

Answer 2

predicted value of Y when X =0

Question 3

slope

Answer 3

Change in Y for one unit change in X

Question 4

Sope coefficient

Answer 4

Cov X Y
/
Variance of X

Question 5

Intercept

Answer 5

Mean Y - B1 x Mean X

Question 6

assumptions

Answer 6

-Linear relaionship
-Variace of error terms is constant (homoskediacity)

homo(same) skediacity

• normal distribution, independant distribution no correlation

Question 7

SSE

Answer 7

Residual - predicted value squared (unexplained)

Question 8

RSS

Answer 8

Predicted val - mean squared (explained)

Question 9

SST

Answer 9

RSS + SSE

Question 10

Anova table

Answer 10

DF
regression RSS=1
Residual SSE =n-2
total SST = n-1

Mean square regression
RSS / DF
mean square error
sse / df

F stat - does single independant variable have explanatory power
MSR / MSE

Rsquared coefficient of determination (how much of the variation have we been able to explain w/independent v and linear relationship)
RSS/ SST (explained / total)
R2 = Pxy2

standard error of estimate = sqr MSE

Question 11

t test

Answer 11

N-2 DF to get t value combined with sig level

slope - hypo value
/
s error

Question 12

confidence interval

Answer 12

Predicted value of Y
Standard Error
N observations

Question 13

functional forms

Answer 13

when no explanatory power in linear relationship

log = relative
lin = absolute

log y lin x
lin log
log log