Regression analysis Topic 11 (part 4)

dummy variables 1 different

INCORPORATING QUALITATIVE (CATEGORICAL) VARIABLES IN REGRESSIONS -categorical independent. variable can be represented in a regression using binary predictors (___) -for a cat.variable with only two possible values, only___ dummy variable is required -examples: yes or no, on or off, male or female -coded as 0 or 1 -regression intercepts are ___ if the variable is significant -assumes the slopes do not change

ri bi independent

-sign of sample correlation coefficient__ same as sign of regression coefficient __ -correlation matrix suggests___variables are not highly correlated w one another

no mild strong severe

0.00=1 ___ varinace inflation 0.50=2.0 __variance inflation 0.90=10.0___ varinace inflation 0.99____variance inflation

levels 1 equals

CATEGORICAL VARIABLES IN REGRESSIONS -more generally, the number of dummy variables needed is number of __of cat. variable -_____ -avoid a dummy variable trap -perfect correlation bw independent. variables in introduced and the last squares regression estimates cannot be obtained if the number of dummy variables __the number of possible categories -excel will not provide an output Pop. regression model Margin=B0+B1(comp.)+B2(awar) +B3(office space)+B4(income)+B5(enroll.)+B6(large city)+E 1 if pop. greater or equal to 200000 0 if pop. in city is less than 200000 estimate: Margin=b0+b1(comp)+b2(A)+b3(O)+b4(I)+b5(E)+b6(1) Margin=b0+b1(C)+b2(A)+b3(O)+b4(I)+b5(E)+b6(0)

drop more instability

CHECKING FOR MULTICOLLINEARITY -one way is to test is to ___ the suspected collinear independent variable from the regression and see what happens to fitted coefficients in re-estimated model -if don't change much, multicollinearity is not a problem -if causes sharp changes in one or ___of remaining coefficients in model, then the multicollinearity may be causing ___

VIFj handout R2j VIFj xj

DETECTING MULTICOLLINEARITY (VARIANCE INFLATIONARY FACTOR) -____-is used to measure collinearity -Formula?______ -___: is the coefficient. of det. when the jth independent. variable is regressed against the remaining k-1 independent variable -if ____>5, __ is highly correlated with the other independent variables

MULTICOLLINEARITY incorrect signs negative neg unstable coefficients low new large small increases

EVIDENCE OF _____ -_____:on the coefficients -expect pos. coefficient based on theory , but in regression is --- -if x1 and x2 are pos. correlated with Y, yet one has a ___ slope in multiple regression -can lead to ___(large standard error and __t value) -large change in the value of previous sign. variables when a new variable is added to the model -a prev significant variable becomes insignificant. when a __variable is added -evidence of instability is when x1 and x2 have high pairwise correlation w Y yet one or both stats have insignificant. t stats in the fitted multiple regression - or the model is significant (___F. test) but individual variables are insignificant (__t statistics) -the estimate of the standard deviation of the model (SE) ___when a variable is added to the model

scatter high correlation

HOW TO CHECK AND SEE IF MULTICOLLINEARITY IS A PROBLEM? A. check estimated coefficients match predicts sign from ___diagrams of independent. and dep. variable B. check for __ correlation bw independent. variables C. Check that estimated coefficients match predicted sign from ___matrix

Multicollinearity independent. redundant NO large low

_______ - high core. exists between two or more ____variables -this means the two variables contribute ___info to the multiple regression model -including two highly correlated independent variables can adversely affect the regression results -__new info provided -standard error of estimates inflated -implying unstable coefficients (___standard error and ___t-values) -coefficient signs may not match prior expectations