Ch. 7: Regression Analysis Flashcards
Regression analysis
Regression analysis reveals the relationship between variables. It’s used to predict the value of dependent (y) variable, based on independent (x) variable
Regression Model
y = β0 + β1x + ε
y=dependent variable
x=independent variable
B0= x-intersept
B1= slope/regression coefficient/marginal effect (shows how to best predict one variable given the othera)
e=epsilon: allows for some random deviation
Everything we don’t have data on…
Everything we don’t have data on, including things we couldn’t possibly ever get data on, are included in our regression in the error term. We assume that the average error is zero.
B1
covariance x and y/variance of x
Bo
bo=y(line)-B1x(line)
avg y-b1*avg x
Marginal effect
b1: increasing the x by 1 increases y by the amount β1.
Best
min(yi-y^i)2
yi: observed value of dependent variable for ith observation-actual data
y^i = estimated value of the dependent variable
for the ith observation- on the regression line
SSR, SSE and SST
ssr: sum of squared deviations based on regression
sse: sum of squared errors/residual
sst: sum of squares total
SST=SSR+SSE
sst
The squared distance between the points (Y) and the mean ( y line ) is the total sum of squares (SST). It’s the sum of squared deviations from before.
ssr
The squared distance between the points on the regression line (Y’) and the mean (Yline) is the sum of squares due to regression (SSR).
R squared/coefficientof determination
r2=SSR/SSTthe percent of the variation in the dependent variable that can be explained by this regression.”
Predictions
y=Bo+B1(X)
