Study on Weight Efficiency of Vehicles: Linear Regression Equation and Analysis, Exams of Data Analysis & Statistical Methods

Download Study on Weight Efficiency of Vehicles: Linear Regression Equation and Analysis and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! Young Final Spring 06 Form A Name:____________________________ Stat 303: Section 503 Spring 2006 Final Exam Form A Instructor: Elizabeth Young Instructions: 1.) Don’t EVEN open this until I tell you. (Meanwhile, read the rest of the instructions.) 2.) TURN IN this form, your cheat sheet, and your scantron. Put your name on everything! 3.) Be SURE to mark your Form on the scantron! 4.) Sign your name on the line on the scantron. With this signature, you agree to follow the Aggie Honor Code: “An Aggie does not lie, cheat, or steal or tolerate those who do.” 5.) There are 25 multiple-choice questions, each worth 5 points. Please mark your answers CLEARLY with a #2 pencil. Multiple marks will be counted wrong. 6.) You have 2 hours to finish this exam. It is worth 25% of your final grade. 7.) Good luck! Young Final Spring 06 Form A Use the following for the next two questions. The weight efficiency of vehicles was the subject of a recent study; when weight was measured in pounds and used to predict fuel efficiency measured in miles per gallon, the linear regression equation was found to be y = 47 – 0.007 x. 1.) What does the number -.007 represent in this equation? A.) If a car increases by one pound, it will get 0.007 fewer miles per gallon. B.) If a car increases by one mile per gallon, it will weigh 0.007 fewer pounds. C.) If a car increases by one pound, it will get 0.007 more miles per gallon. D.) If a car weighs 0 lbs, our equation predicts that it will get -0.007 miles to the gallon. E.) The correlation between car weight and fuel efficiency is -0.007. 2.) Suppose your car weighs 2500 lbs. How many miles per gallon would this equation predict it to get? (We’re just looking for the point estimate here; don’t worry about confidence intervals here.) A.) -0.007 B.) 47 C.) 29.5 D.) 32.4 E.) 34.2 This chart is from a study in which doctors were randomly placed into two groups: one to take aspirin every day, and the other to take a placebo. (Yes, the doctors were the patients in this study!) Neither the doctors taking the drugs nor the physicians examining them knew whether the doctor was taking the placebo or the aspirin. The chi-squared test statistic was 28.3, with a corresponding p-value less than 0.001. 3.) What is true about this study? A.) We can say that the aspirin caused the doctors taking it to have a lower rate of myocardial infarctions. B.) We cannot say that there is a cause-and-effect relationship between aspirin and myocardial infarction, because lurking variables are a huge problem with observational studies like this one. C.) Since my p-value was less than 0.001, I cannot reject, concluding that whether a person has a heart attack is not related to which medicine is taken. D.) A and C above Heart Attack Group Yes No Total Placebo 190 10,840 11,030 Aspirin 100 10,930 11,030 Total 290 21,770 22,060 Young Final Spring 06 Form A Multiple R-Square Adjusted StErr of Summary R R-Square Estimate 0.8853 0.8771 20.71547269 Degrees of Sum of Mean of F-Ratio p-ValueANOVA Table Freedom Squares Squares Explained 46385.91867 46385.91867 < 0.0001 Unexplained 6007.831325 429.130809 Coefficient Standard t-Value p-Value Confidence Interval 95% Regression Table Error Lower Upper Constant - 9.277108434 12.09620168 0.4559 - 35.22088077 16.66666391 age 21.14457831 2.033765121 < 0.0001 16.78258595 25.50657067 Use the following to answer the next 6 problems. A department store chain wanted to know when to replace its old registers, so it kept records on maintenance costs and age of the registers. Using a random sample of 16 registers, they ran a linear regression; below is the output. Scatterplot of Residual vs Fit -40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 0.0 50.0 100.0 150.0 200.0 250.0 Fit R e s id u a l StatTools Student Version For Academic Use Only Young Final Spring 06 Form A Q-Q Normal Plot of Residual / resids -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 Z-Value S ta n d a rd iz e d Q -V a lu e 9.) What conclusions can we draw from the output? A.) Age and maintenance costs have a positive relationship. B.) The slope is not significantly different from 0. C.) The correlation between age and maintenance costs is -0.94. D.) The estimate of the slope, b1, is -9.2771. E.) Two of the above are true. 10.) Do you think the assumptions for running a linear regression are met? A.) It looks like the data is definitely not normally distributed; it seems to have a heavy right skew. B.) The constant variance assumption is definitely not met. C.) The mean zero assumption is not met; they should have used a higher-order polynomial. D.) We know for sure that they should not have run a linear regression with this data; the residual plot shows that there is definitely not a linear relationship between the variables. E.) It looks like all the assumptions are met! 11.) What is the test statistic for testing whether the slope is 0 for this problem? A.) 108.0927 B.) -0.7669 C.) -9.277 D.) 10.3968 E.) 21.1445 Young Final Spring 06 Form A 12.) What is a description of Type I error for the hypothesis test for the slope in this problem? A.) Concluding that the slope is positive when actually it is negative. B.) Concluding that the slope is not zero when actually it is not zero. C.) Concluding that the slope is not zero when actually it is zero. D.) Concluding that the slope is zero when actually it is not equal to zero. E.) Concluding that the slope is zero when actually it is positive. 13.) What degrees of freedom should we use for the regression (the explained degrees of freedom, aka model df)? A.) 1 B.) 2 C.) 3 D.) 4 E.) 14 14.) What is the F-statistic for testing whether the regression model is significant? A.) 108.0927 B.) 46385.91867 C.) 429.130809 D.) 0.99083 E.) 7.7209 Use the following for the next three questions. An agricultural economist wanted to know how much fertilizer was the most economically advantageous to use for a new strain of corn. To that end, he randomly assigned different levels of fertilizers (measured in cups per plot) to different corn plant plots, and measured their yield (in bushels) at the end of the growing season. The output from the regression is shown below. Degrees of Sum of Mean of F-Ratio p-ValueANOVA Table Freedom Squares Squares Explained 840.9051473 158.9252 < 0.0001 Unexplained 25 132.2800378 Coefficient Standard t-Value p-Value Confidence Interval 95% Regression Table Error Lower Upper Constant 21.36423841 1.042244289 20.498 < 0.0001 19.21769612 23.51078071 fertilizer 3.277199622 0.259960008 12.607 < 0.0001 2.741801963 3.81259728 Young Final Spring 06 Form A 20.) A librarian wanted to know whether being a child or an adult was related to the type of book checked out (biography, fiction, nonfiction). (The library only kept track of whether the person checking the book out had a child or adult library membership.) What hypotheses should he set up? A.) Ho: μ1 = μ2 = μ3, where μ1, μ2, and μ3 are the mean number of children’s books checked out from the biography, fiction, and nonfiction sections. vs. Ha: μ1 ≠ μ2 ≠ μ3 B.) Ho: μ1 = μ2 = μ3, where μ1, μ2, and μ3 are the mean number of children’s books checked out from the biography, fiction, and nonfiction sections. vs. Ha: at least one mean is different from the others. C.) Ho: μ1 = μ2, where μ1 and μ2 are the mean number of books checked out by children and adults vs. Ha: μ1 ≠ μ2. D.) Ho: type of book and age are independent vs. Ha: type of book and age are dependent. E.) Ho: β1 = 0 vs. Ha: β1 ≠ 0, where β1 is the slope of a regression line for the variables type of book and age range. 21.) In a roulette game at Billy Bob’s house, players gain $1.00 for red spaces and lose $1.00 for green and black spaces. The earnings and their probabilities thus have the following distribution: Earnings 1 -1 Probability 0.4737 0.5263 How much money does Bubba expect (on average over the long run) to make in a single spin of the wheel? A.) $0.4737 B.) -$0.4737 C.) -$0.0526 D.) -$0.0648 E.) $0.0648 22.) Suppose X ~ N(3, 62) and Y ~ N(4, 72). What is the distribution of X + Y, if X and Y are independent? A.) N(7, 9.222) B.) N(1, 3.612) C.) N(1, 122) D.) N(7, 92) E.) N(7, 132) Young Final Spring 06 Form A 23.) In a hypothesis test of Ho: μ = 6 vs. Ha: μ ≠ 6, a simple random sample of 25 is drawn from a normally distributed population with known standard deviation σ = 5. The sample mean is found to be x = 7.2. Which of the following is closest to the p-value for this test? (Draw a picture! Mama said!) A.) 0.8849 B.) 0.1151 C.) 0.2302 D.) 0.0576 E.) 0.2496 24.) The following confidence intervals for a proportion were found. For testing the hypotheses Ho: π = 0.5 vs. Ha: π ≠ 5, what is a range for my p-value? 99%: (0.22, 0.52) 98%: (0.23, 0.51) 95%: (0.25, 0.49) 90%: (0.27, 0.47) A.) 0.10 < p-value B.) 0.05 < p-value < 0.10 C.) 0.02 < p-value < 0.05 D.) 0.01 < p-value < 0.02 E.) p-value < 0.01 25.) What are you going to do this summer? (Only pick one; you’ll get it wrong otherwise!) A.) work B.) sleep C.) swim D.) watch TV E.) take classes 1 A 2 C 3 A 4 D 5 D 6 A 7 E 8 A 9 A 10 E 11 D 12 C 13 A 14 A 15 B 16 B 17 E 18 B 19 E 20 D 21 C 22 A 23 C 24 C 25 A