ST 412/512 – Midterm Exam w: Key (00) – Methods of Data Analysis II

St 412/512, D. Schafer, Spring 2000EXAMYour name:_____SOLUTIONS________________________________Your lab time (Circle one): Tues. 8:00 Tues 11:00 Tues 2:00This is a 50-minute open-book, open-notes test. Show work where appropriate.Part A. Write the letter from the list below that best matches the description. (4 pointseach)1. __T__ The quantity that least squares estimators minimize.2. __R__ Another name for the estimate of σ 2 in regression analysis.3. __S__ A residual divided by its estimated standard deviation.4. __J__ An explanatory variable that takes on the value 1 or 0.5. __F__ An inference about the regression in a region outside of the range of observed x’s.6. __W__ The distance, in standard errors, between an estimate and a hypothesized value.7. __O__ An interval of plausible values of the response at specified explanatory variable values.8. __M__ A test for checking model adequacy when there are replicate responses.9. __Z__ A statistic used to identify problems of multicollinearity.10.__D__ A statistic for comparing models with different sets of possible x’s.A. Calibration interval J. Indicator S. Studentized residualB. Confidence interval K. Interaction T. Sum of squared residualsC. Cook’s Distance L. Interpolation U. Sum of squares due to regressionD. Cp statistic M. Lack-of-fit F-test V. t-ratioE. Extra sum of squares N. Leverage W. t-statisticF. Extrapolation O. Prediction interval X. Total sum of squaresG. Fitted value P. Quadratic term Y. VarianceH. F-statistic Q. Residual Z. Variance inflation factorI. F-word R. Residual mean squarePage 1 of 5

Part B. Acorn data (questions worth 6 points each). Below is a plot ofY = log of the species range area (100×km 2 ), versusX 1 = log of the acorn (seed) volume (cm 3 )for species of oak trees from Atlantic and California regions. The species with the smallest Y(species #7) is only found on an island so its range area cannot possibly exceed the area of theisland.log of Range Area4 6 8 10Regionwith # 7without #7AtlanticCaliforniaspecies # 7-1 0 1 2 3Log of Acorn Size11. Based on the scatterplot, circle the letter for the one sentence that describes the probableinfluence of species # 7.a) The species is probably not influential.b) The interactive effect of log acorn size and region (Atlantic or California) is substantiallymore significant when the species is included than when it is not included.c) The interactive effect of log acorn size and region is substantially less significant when thespecies is included than when it is not included.Page 2 of 5

19. The following is the fit to model D (recall: Y = log area, X 1 = log acorn volume):µ(Y|X 1 ,X 2 ) = 5.7 + 2.8X 1 + .63X 2 .Which of the following is the best interpretation of the effect of acorn volume.SHOW WORK then circle the correct answer.2.82 = 7.0see p. 208a) Associated with each one cm 3 increase in acorn volume is a 2.8 ×100 km 2 increase in the meanrange area.b) Associated with each one cm 3 increase in acorn volume is a .63×100 km 2 increase in the meanrange area.c) Associated with each doubling in acorn volume is a 2.8 ×100 km 2 increase in the mean rangearea.d) Associated with each doubling in acorn volume is a .63 ×100 km 2 increase in the mean rangearea.e) Associated with each doubling in acorn volume is a 1.9 ×100 km 2 increase in the mean rangearea.f) Associated with each doubling in acorn volume is a 7-fold change in the median range area.g) Associated with each doubling in acorn volume is a 16-fold change in the median range area.20. Suppose there are 3 regions. Let X 2 = 1 if a species is from the Atlantic region, and 0 otherwise;let X 3 = 1 if a species is from the midwest region and 0 otherwise; and let X 4 = 1 if aspecies is from the California region, and 0 otherwise. Write down a model that specifies 3parallel lines for the regression of Y on X 1 , using the midwest region as the “reference level.”µ(Y|X 1 ,X 2 ,X 3 ,X 4 ) = β 0 + β 1 + β 2 X 2 + β 3 X 4_____________________________Page 5 of 5

POINT DISTRIBUTION SUMMARYLower quartile = 69.5Median = 73Upper quartile = 84LETTER GRADE SCORINGA 84-100A- 77-83B+ 70-76B 60-69B- 50-59C+ 40-59C 35-39Page 6 of 5