# statistics

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The scatter diagram of midterm scores and final scores in a large class is football shaped. For about 80% of the students, the regression estimate of final score based on midterm score is correct to within 15 points. For about 95% of the students, the regression estimate of final score based on midterm score is correct to within how many points?

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It has to be 21

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why 21?

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22.95

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80% is between -1.2815 and 1.2815 in standard units
90% is between -1.96 and 1.96

15/r.m.s. error = 1.2815
score/r.m.s. error = 1.96

=> score = 15*1.96/1.2815

Now, when rounding 1.2815 to either 1.281 or 1.282 you'll get slightly different result

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