課程名稱︰統計學一下 課程性質︰必修 課程教師︰王衍智 開課學院：管理學院 開課系所︰財務金融學系 考試日期（年月日）︰101.06.13 考試時限（分鐘）：90 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Statistic II Mock exam 2 Time:18:30~20:00 Part I : Multiple choices questions (3 points for each) 1. In a multiple regression with five explanatory variables, data are collected on 63 observations. What are the degrees of freedom for the ANOVA F test? A) 4 and 57 B) 5 and 57 C) 5 and 58 D) 5 and 62 2. In a multiple regression with two explanatory variables, the total sum of squares SST=1000 and the mean square error MSE=40.There are 13 observations. What is the value of R^2? A) 0.04 B) 0.52 C) 0.60 D) 0.96 3. Which one of following statements is true? A) ANOVA can be used only if the number of observations per group is equal. B) The ANOVA is used to test the hypothesis that the group variances are equal. C) The analysis of variance is used to test for differences between sample means when comparing two or more means. D) We always do contrast test between groups before ANOVA. 4. Suppose that examination of the residual plots from an ANOVA indicate serious problems with both normality and homogeneity of variances. What might you do to provide a solution to this problem? A) Transformation of the dependent variable. B) Transformation of the independent variable. C) Transformation of the dependent and independent variables. D) Use contrast test. 5. A study compares three levels of Factor A and two levels of Factor B, with five observations in each cell. What are the degrees of freedom for the F statistic that is used to test for interaction? A) 2 and 24 B) 3 and 30 C) 5 and 6 D) 6 and 24 Use the following to answer questions 6-8: A researcher wished to compare the effect of the different rates of stepping on volunteers' heart rates in a step-aerobics workout. A collection of 30 adult volunteers, 15 women and 15 men, were selected from a local gym. The men were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout with Group 1 at a low rate of stepping, Group 2 at a medium rate of stepping, and Group 3 at a rapid rate. The mean heart rate at the end of the workout for all the subjects was determined in beats per minute. A partial ANOVA table for these data is given below: Source Sum of Squares DF Mean Square F P-value Group 2553.2 Gender 70.7 70.7 Group*Gender 231.7 0.48 0.623 Error 5762.0 Total 8617.6 6. What are the factors in this experiment? A) Rate of stepping and heart rate. B) Rate of stepping and gender. C) Heart rate and gender. D) Gym membership and gender. 7. What are the advantages of studying the two factors simultaneously in the same experiment? I. It is more efficient to study two factors simultaneously rather than separately. II. We can reduce the residual variation in a model by including a second factor thought to influence the response. III. We can investigate the interaction between factors. A) I B) III C) I and III D) I,II, and III. 8. What is the value of the F statistic for testing the main effect of gender? A) 0.01 B) 0.29 C) 5.32 D) 81.49 9. Which of the following statements about logistic regression is NOT true? A) The variable we ate trying to model is categorical and has only two possible values, i.e., “success” or “failure”. B) The explanatory variable can be either categorical or quantitative. C) Logical regression makes use of the odds of the binomial outcome“success”, ps/(1-ps). D) The statistical model is given by : ps/(1-ps) = β0+β1x 10. In simple random sample, 320 stay-at-home mothers are interviewed. The questions are all about their hobbies outside of raising their children. The number of mothers in the sample who enjoy reading in their spare time is 223. What are the odds that a stay-at-home mother enjoys reading? A) 0.303 B) 0.435 C) 0.697 D) 2.3 Part II: Calculations (5% for each answer) 11. Taipei City investigated A, B, and C districts and their average income(y). Five households are randomly sampled for each district. Data are: A B C Average Income 31 38 33 Income S.D. 4 3.317 3.464 i) Please use one-way ANOVA and test the null hypothesis thatμA=μB=μC. (F(α.0.05)=3.89) ii) If research believes μA>μB=μC (the alternative) and test null hypothesis ofμA=μB=μC. Please use contrast test to examine this hypothesis (set test statistics c=μA-0.5μB-0.5μC and t(α=0.025)=2.18) 12. Given an AR(1) model: Yt = 0.8 Yt-1 + Et, in which Et i.i.d~N(0,σ^2) if we transform the AR(1) to MA(n): Yt=a+b0Et + b1Et-1 + b2Et-2 + b3+Et-3 ….. i) Please find coefficients of first four MA orders (i.e., b0~b3) ii) Please find intercept a if we expend n approaching infinite. 13.Researcher studies the number of holidays per month (y) for IT industry. Two determinants on holidays are examined: salary(x1) and number of kids(x2). The researcher randomly sample 8 works and data are: ID 1 2 3 4 5 6 7 8 Yi 0 5 0 4 3 8 9 7 x1i 3 5 6 6 5 6 6 7 x2i 6 4 7 2 1 1 1 2 The regression model is specified : y=a0+a1x1+a2x2+e. i) Please find a0, a1, and a2 estimates. ii) Please find R^2 and adjusted R^2 if SSR=58.44 14. GameXper Inc. is interested in the effect of gender on the choice of its newly developed game. The survey shows preference of men and women below. The marketing sector plans to use logistic regression model to carry out the analysis. Like Dislike Men 70 30 Women 60 40 i) Please write down the logistic regression model setting. ii) Please compute odds ratios for men and women. iii) Please solve the parameters of the logistics model. 15. Given following rime series data yt, please answer following questions. T 1 2 3 4 5 6 7 8 9 Yt 1 2 5 6 7 4 8 9 12 i) We specify yi = a + b*t + et. Please find a and b. ii) We specify yi = c + dyt-1 + et. Please find c and d. ^ iii) Please find y10 by using moving average of order 3 (MA(3)). Part III: Proof(10%) 16. Given an AR(1) model: yt = a0 + a1*yt-1 + et, et~(0,1). Please prove i) E(y) = a0/ (1-a1) ii) Var(y) = 1 / (1-a1^2) if a0=0. --

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