# 17.2 – Pat Statsdud, a student ranking near the bottom of the statistics class, decided that a certain amount of studying …

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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