STA 6166 – Exam 3 – Fall 2009 PRINT Name _____________________A study was conducted to relate weight gain in chickens (Y) to the amount of the amino acid lysine ingested by the chicken (X). A simple linear regression is fit to the data.- Give the fitted equation, and the predicted value for X=0.20- Give a 95% Confidence Interval for the MEAN weight gain of all chickens with X=0.20 (Note: the mean of X is 0.16 and SXX=0.020)- What proportion of the variation in weight gain is “explained” by lysine intake?A researcher reports that the correlation between length (inches) and weight (pounds) of a sample of 16 male adults of a species is r=0.40. - Test whether she can conclude there is a POSITIVE correlation in the population of all adult males of this species: o H0: - = 0 HA: - > 0o Test Statistic: o Rejection Region (-=0.05):o Conclude: Positive Association or No Positive Association- A colleague from Europe transforms the data from length in inches to centimeters (1 inch=2.54 cm) and weight from pounds to kilograms (1 pound=2.2 kg). What is the colleague’s estimate of the correlation?An additive for interior house paint has been developed that greatly increases the ability of the paint to resist stains. A study is conducted to determine whether it is safe when children are exposed to it. Various amounts are fed to test animals,and animals were classified as having developed liver tumors or not. The following results were obtained from a logistic regression analysis.- Give the predicted probability of an animal developing a liver tumor when the dose=100.- What can you conclude about the association between dose and probability of the animal developing liver tumor at the - = 0.05 significance level? Positive / Negative / No Association- By how much (multiplicatively) do the odds of an animal developing a liver tumor change when dose is increasedby 1 unit (give the point estimate).Late at night you find the following SPSS output in your department’s computer lab. The data represent numbers of emigrants from Japanese regions, as well as a set of predictor variables from each region.Model SummaryModel R R SquareAdjusted RSquareStd. Error ofthe Estimate1.525(a) .275 .222 181.89029a Predictors: (Constant), PIONEERS, LANDCULT, AREAFARMANOVA(b)Model Sum ofSquares df Mean Square F Sig.1 Regression514814.087 3 171604.696 5.187 .004(a) Residual1356447.158 41 33084.077 Total1871261.244 44 a Predictors: (Constant), PIONEERS, LANDCULT, AREAFARMb Dependent Variable: EMGRANTSCoefficients(a)Model UnstandardizedCoefficientsStandardizedCoefficients t Sig. B Std. Error Beta 1 (Constant)407.070 226.341 1.798 .079 LANDCULT-1.685 3.567 -.069 -.472 .639 AREAFARM-2.132 1.056 -.299 -2.019 .050 PIONEERS175.968 61.222 .391 2.874 .006a Dependent Variable: EMGRANTSa) How many regions are there in the analysis? _______________________b) Give the test statistic and P-value for testing (H0) that none of the predictors are associated with EMGRANTS____________________c) Give the test statistic and P-value for testing whether LANDCULT is associated with EMGRANTS, after controlling for AREAFARM and PIONEERS_____________________d) What proportion of the variation in EMGRANTS is “explained” by the model? ___________________e) Give the estimated regression equation ________________________________________________A realtor is interested in the determinants of home selling prices in his territory. He takes a random sample of 24 homes that have sold in this area during the past 18 months, observing: selling PRICE (Y), AREA (X1), BEDrooms (X2), BATHrooms (X3), POOL dummy (X4=1 if Yes, 0 if No), and AGE (X5). He fits the following models (predictor variables to be included in model are given for each model):Model 1: AREA, BED, BATH, POOL, AGE SSE1 = 250, SSR1 = 450 Model 2: AREA, BATH, POOL SSE2 = 325, SSR2 = 375 a) Test whether neither BED or AGE are associated with PRICE, after adjusting for AREA, BATH, and POOLat the -=0.05 significance level. That is, test:0/0:0:52520orandHvsHA b) What statement best describes -4 in Model 1? a) Added value (on average) for a POOL, controlling for AREA, BED, BATH, AGE b) Effect of increasing AREA by 1 unit, controlling for other factors c) Effect of increasing BED by 1 unit, controlling for other factors d) Effect of increasing BATH by 1 unit, controlling for other factors e) Average price for a house with a POOLAmong a group of 100 children exposed to a petting zoo, 20 contracted a particular symptom. Among a second group of 100 children not exposed to the petting zoo, 12 contracted the symptom. Give the estimated odds ratio (exposed group divided by not exposed group), and the corresponding 95% confidence interval for the population odds ratio. What do youconclude at the ------ significance level? Zoo increases odds / Zoo decreases odds / No association
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