chpt 15 review Flashcards
What is multiple linear regression used for
more than 2 i.v
the variance of the error term E is assumed to be what
the same for all i.v
Values of E are
- independent of each other
2. E is assumed to be normally distributed
What is the dependent variable called in the multiple linear regression
the response variable
what is the graph called in multiple linear regression
the response surface
What does MSE provide in multiple linear regression
provides an unbiased estimate of Q2 (variance of the error term)
What is the null hypothesis for the MSE in multiple linear regression
Ho: B1=B2=Bp= 0
MSE s/b close to 1
If Ho: B1=B2=Bp=0 is false, then MSR overstates Q2
MSR/MSE becomes larger
What is the adjusted R2 (or adjusted coefficient of determination)?
used for more than one I.V.
r2 always increases as more variables are added
- used to avoid overestimating r2
what is the formula for R2 adjusted
see sheet
what tests can we use for testing significance in Multiple linear regression?
T-test and the F-test
what is the T- test used for in multiple linear regression
test for INDIVIDUAL significance
- separate test is used for I.V.
What is the Null and alternative hypothesis for t-test in multiple linear regression
Ho: Bi = 0
Ha: Bi does not equal 0
If we reject Ho in the t-test for multiple linear regression, what can we say
that xi is significant
What is the degrees of freedom for the t test in multiple linear regression
same as SSE df - n-p-1
p- represents =
What is the F test used for in Multiple linear regression
used to test the OVERALL significance of the model
What is the null hypothesis for the F- test in multiple linear regression
Ho: B1=B2=Bp=0
Ha: one or more of the parameters is not equal to 0
What can you say if you reject Ho in an F test for multiple linear regression
conclude 1 or more than one of the parameters is not = 0
- overall relationship b/w x and y is significant
If we do not reject Ho in the F-test for multiple linear regression, what can be said
we do not have sufficient evidence to conclude a significant relationship is present
If the F- test in Multiple regression shows overall significance what can we do
a t-test on individual B1 to determine if B1 = 0
if we cannot reject Ho what can this mean?
- could be that w x2 already in the model, x 1 does not make a significant contribution to determining the value of y
What is multicollinearity
correlation among the individual variables
What can you do to try to avoid multicolinearity
try to not include i.v. s that are highly correlated to each other. in practice this is rarely possible
What is the Rule of thumb for Rxy in Multicollinearity
- greater than +.7 or less than -.7 for 2 i.v., this is a Warning sing of potential problems
