STA 6127 – Exam 3 – Spring 2010 PRINT Name __________________________Q.1. A linear regression model is fit, relating Y=Math Score on a standardized exam to Age and Education level. The following output gives the results of the regression model. Complete the parts below the output. The model is: E(Y) = AAGEEEDUp.1.a. Give the predicted score for a child whose AGE=12.0 and EDU = 6. ________________________p.1.b. Give the test statistic and P-value for testing H0: A=E=0 Test Stat ________ P-Value ______p.1.c. Give the test statistic and P-value for testing H0: A=0 Test Stat ________ P-Value ______p.1.d. Give the test statistic and P-value for testing H0:E=0 Test Stat ________ P-Value ______p.1.e. Which statement best describes the results of the experiment (Choose only one)i) Neither Age or Education are associated with math scoresii) Adjusting for Age, Education is associated with math scoresiii) Adjusting for Education, Age is associated with math scoresiv) As a “group” of variables, Education and Age are associated with math scoresp.1.f. This appears to be an example where multicollinearity exists Yes or NoQ.2. A regression model is fit with 4 predictor variables and 24 observations. p.2.a. Above what value (in absolute valuable) would the DFBETAS measure for an individual case to be for us to feel that that case has highly influenced that regression coefficient?p.2.b. Above what value (in absolute valuable) would the DFFITS measure for an individual case to be for us to feel that that case has highly influenced that cases predicted value?Q.3. A logistic regression model is fit, relating whether a coupon is redeemed (Y=1, if yes, 0 if not) to the Valueof the coupon (V=$5, $10, $15, $20) for a product with a base price of $75. The estimated regression coefficients and statistics are given below for the model: log(odds(redeem)) = Vp.3.a. Give the (Wald) Test statistic, Rejection Region, and P-value for testing H0:  = 0 vs HA: ≠0. Test Statistic ____________ Rejection Region _____________ P-value _______________p.3.b. Give the fitted probabilities for a coupon to be redeemed when the Value is $5 and when $20:20^5^Q.4. Two regression models were fit, relating advertising price for newspaper ads (Y in $) to circulation (X in 10000s). The authors fit a linear regression and quadratic regression relating Y to X, based on n=160 papers. Test H0: The relationship is linear ( vs HA: The relation is nonlinear (≠at the = 0.05 significance level. For the model: E(Y) = 1 X X29369.003.0703.49274.0525.72Linear2Quad^2LinearLinear^ RXXYRXY p.4.1.: Test Statistic:p.4.b. Rejection Region: Test Statistic > or < ____________________p.4.c. Do you conclude that the relationship is not linear? Yes or NoQ.5. A survey measured Chinese residents willingness to engage in rightful resistance to local authorities (Y=1 if Yes, 0 if No). The independent variables were:Age, Male(yes=1,no=0), Education, Annual Household Income, Party Member (yes=1,no=0), PLA Vet (yes=1,no=0), More Trust in high levels of government than low levels (interval scale) For the null model: log(odds(Y=1)) = , -2logL = 619.77.  For the full model: log(odds(Y=1)) = Age + … + 7 TrustHigh, -2logL = 523.89p.5.a. Test H0:  versus HA: Not all i = 0Test Statistic ______________ Rejection Region ______________ P-Value < or > 0.05p.5.b. Controlling all other factors, the odds of a male engaging in rightful resistance is ________ times the odds of a female engaging in rightful resistancep.5.c. If you ran backward elimination with SLS=0.05, which factor would be the first to be eliminated? Hint: Compare the smallest (B/SE)2 with the critical chi-square value with 1 degree of freedom.Factor eliminated ___________________ because ________ < or > ________________Q.6. An ordinal regression model is fit, relating a quality relating of beer (Y=Good (3),Fair(2),Poor(1)) to the price the rater was told it cost (X=$2,$3,$4). Note, in reality it was always the same beer. A model is fit, where: 2,1)(oddslog  jXjYjParameter EstimatesEstimate Std. Error Wald df Sig.95% Confidence IntervalLowerBound Upper BoundThreshold [quality = 1.00000] .076 .368 .043 1 .836 -.646 .798[quality = 2.00000] 1.794 .395 20.655 1 .000 1.021 2.568Location price .418 .171 5.953 1 .015 .082 .754Link function: Logit.p.6.a. Complete the following table of fitted Probabilities:p.6.b. The Pearson Goodness-of-fit statistic for this model, compared to the saturated model which fits 6 distinct logits to the first 2 rows of the above table (and perfectly fits the sample data) is equal to 1.294 which under the null hypothesis that our regression model is appropriate has a P-value of 0.731 (based on chi-square distribution with 3 df (6 logits – 3 Parameters in our model). Do you feel our model is appropriate? Yes or