Regression
Best line has overall smallest residuals
minimizes the sum of squares of the residuals
!
r2 represents the percentage of the variance in y
that can be explained by changes in x - tells us how good line is (0-1)
to test how good b0 and b1
Conf Int
Hypothesis Test
Residual normally distributed
mean = 0
SD =
Also called "s" or standard error of line
In neumerator = SS or Residuals
Den = dof of residuals
Confidence Interval
t (n-2) dof
Hypothesis Test
\
b-0 cause of null hypothesis
dof (n-2)
Defs
Suppose we want to measure the effect of household size
(predictor) on the number of cars owned by the household
(dependent variable)
X t by 2 - two sided test
In a regression, b1 or b0 are significant (i.e. null hypothesis
rejected), if and only if, the C=1-alpha interval does not
contain 0.
ANOVA
Mean Square - It gives us a sense of the average degree of variation along the regression line, and the residual.
SS / dof
F stat
P val= sig of F - for b1