標題:
統計學問題3 help.... thx>.
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發問:
Mr Wong would like to analyze the relationship between the hours of study and the marks in the QT exam of his students. The following table shows the relevant data from a sample of 12 student. hours of study24, 8, 35, 27, 6, 11, 14, 22, 38, 27, 13, 9marks in the exam60, 42, 75, 61, 32, 38, 50, 58,... 顯示更多 Mr Wong would like to analyze the relationship between the hours of study and the marks in the QT exam of his students. The following table shows the relevant data from a sample of 12 student. hours of study 24, 8, 35, 27, 6, 11, 14, 22, 38, 27, 13, 9 marks in the exam 60, 42, 75, 61, 32, 38, 50, 58, 65, 70, 45, 40 a) indicate the independent variable in the case above. b) develop the regression equation. c) calculate the coefficient of correlation. Comment on the relationship between the two variables. d) predict mark in the exam of a student if he studies 48 hours for the exam. Comment on the prediction.
最佳解答:
a) independent variable is "hours of study" (hours). b) marks_hat = 29.78428 + 1.19055*hours c) correlation (r) = 0.9370 The two variables are strongly and positively correlated with each other. d) 29.78428 + 1.19055*(48) = 86.93068 The student will score 86.93 in the QT exam if he studies 48 hours for the exam. Recall that the sample data of the independent variable lies between 6 and 38. Since 48 hours of study is outside the range of the given sample, the prediction may not be correct. 2009-01-05 15:05:38 補充： If you calculate part b and c by hand, the followings are the steps. sum of hours = 234 sum of marks = 636 sum of hours^2 = 5854 sum of marks^2 = 35792 sum of hours*marks = 13939 2009-01-05 15:05:58 補充： b) cov(hours,marks) = 13939-234*636/12 = 1537 var(hours) = 5854-234*234/12 = 1291 beta1 = cov(hours,marks)/var(hours) = 1537/1291 = 1.19055 beta0 = mean(marks)-beta1*mean(hours) = 636/12-1.19055*234/12 = 29.78428 2009-01-05 15:06:05 補充： c) sd(hours) = sqrt(1291) = 35.93 var(marks) = 35792-636*636/12 = 2084 sd(marks) = sqrt(2084) = 45.65 r = beta1*sd(hours)/sd(marks) = 1.19055*35.93/45.65 = 0.9370
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