17.2 – Pat Statsdud, a student ranking near the bottom of the statistics class, decided that a certain amount of studying could actually improve final grades. However, too much studying would not be warranted, since Pat’s ambition (if that’s what one could call it) was to ultimately graduate with absolute minimum level of work. Pat was registered in a statistics course, which had only 3 weeks to go before the final exam, and where the final grade was determine in the following way: Total mark = 20% (assignment) + 30% (midterm) + 50% (final exam) To determine how much work to do in the remaining 3 weeks, Pat needed to be able to predict the final exam mark on the basis of the assignment mark (worth 20 points) and the midterm mark (worth 30 points). Pat’s marks on these were 12/20 and 14/30, respectively. Accordingly, Pat undertook the following analysis. The final exam mark, assignment mark, and midterm test mark for 30 students who took the statistics course last year were collected. Final (y) Assignment (x1) Midterm (x2) 23 15 11 49 15 28 34 13 19 43 20 26 43 20 22 29 18 13 31 20 10 30 10 11 36 13 16 33 16 15 39 19 16 33 20 16 24 10 12 36 12 22 29 10 13 43 15 23 50 12 28 40 14 20 42 11 20 35 13 15 31 15 10 48 19 30 42 13 16 37 13 24 40 18 20 30 10 16 25 20 10 33 11 18 30 12 13 25 14 15
A) Determine the regression equation. B) What is the standard error of estimate? C) What is the coefficient of determination? What does this statistic tell you? D) Test the validity of the model. E) Interpret each of the coefficients. F) Can Pat infer that the assignment mark is linearly related to the final grade in this model? G) Can Pat Infer that the midterm mark is linearly related to the final grade in this model? H) Predict Pat’s final exam mark with 95% confidence.
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