課程名稱：統計學 課程性質：整開 課程範圍：主要以期中考後為主，i.e., Chapters 14 - 18. 開課教師：丁兆平 開課學院：商學院 開課系級：統計系 考試日期(年月日)：2014/6/24 考試時限(Mins)：120 min 附註： 所有檢定均需寫出 H0, H1, α, Test Statistic, Rejection Region or p-value, and Conclusion. 試題本文： 1. The administrator of a new paralegal program at Seagate Technical College wants to estimate the grade point average in the new program. He thought that high school GPA, the verbal score in the Scholastic Aptitude Test (SAT), and the mathematics score on the SAT would be good predictors of paralegal GPA. The data on nine students are: Student High School GPA SAT Verbal SAT Math Paralegal GPA 1 3.25 480 410 3.21 2 1.80 290 270 1.68 . . . . . . . . . . 9 2.63 469 440 2.33 a. Write out the regression equation (or the model). (5 pts) b. Consider the following correlation matrix. Which variable has the strongest correlation with the dependent variable? Some of the correlations among the independent variables are strong. Does this appear to be a problem? (5 pts) p-gpa h-gpa verbal h-gpa 0.911 verbal 0.616 0.609 math 0.487 0.636 0.599 c. Consider the following output. Compute the coefficient of multiple determination. (5 pts) The regression equation is P-GPA = -0.411 + 1.20 H-GPA + 0.00163 Verbal - 0.00194 Math Predictor Coef SE Coef T P Constant -0.411 0.7823 -0.53 0.622 H-GPA 1.2014 0.2955 4.07 0.010 Verbal 0.001629 0.002147 0.76 0.482 Math -0.001939 0.002074 -0.94 0.393 Analysis of Variance SOURCE DF SS MS F P Regression 3 4.3595 1.4532 10.33 0.014 Residual Error 5 0.7036 0.1407 Total 8 5.0631 d. Conduct a global test of hypothesis from the preceding output. Does it appear that any of the regression coefficients are not equal to zero? Let α =0.05. (10 pts) e. Conduct a test of hypothesis on each independent variable. Would you consider eliminating the variables "verbal" and "math"? Let α = 0.05. (10 pts) 2. The health of the construction industry is often an indication of the health of the economy. The data (in 1000) below show the number of bricks produced of quarter for 2005 to 2011. Quarter ----------------------------------------------------------------- Year I II III IV 2005 210 180 60 246 2006 214 216 82 230 2007 246 228 91 280 2008 258 250 113 298 2009 279 267 116 304 2010 302 290 114 310 2011 321 291 120 320 a. Determine the typical seasonal patterns for sales using the ratio-to-moving method. (15 pts) b. Deseasonalize the data and determine the trend equation. (15 pts) c. Project the brick production for 2012, and then seasonally adjust each quarter. (5 pts) 3. The accompanying data refers to concentration of the radioactive isotope strontium-90 in milk samples obtained from five randomly selected dairies in each of four different regions. Region ---------------------------------------------------------------------- 1 2 3 4 ---------------------------------------------------------------------- 6.4 7.1 5.7 9.5 5.8 9.9 5.9 12.1 6.5 11.2 8.2 10.3 7.7 10.5 6.6 12.4 6.1 8.8 5.1 11.7 Test at level 0.1 to see whether the stronitium-90 concentration is the same for all four regions. (15 pts) 4. Each individual in a random sample of high school and college students was cross classified with respect to both political views and clubbing frequencies, resulting in the data displayed in the accompanying two-way table. Does the data support the hypothesis that political views and clubbing frequencies are independent? Test the appropriate hypothesis using level of significance 0.01. (15 pts) Clubbing Frequency Never Rarely Frequently Political | Liberal 479 173 120 views | Conservative 214 47 15 | Other 172 45 85 --

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