In the athletics event known as the shot put, male competitors \"put\" the \"sho

Question

In the athletics event known as the shot put, male competitors "put" the "shot," a 16-pound metal ball. (Female competitors use a smaller shot.) In the United States, high school male competitors put a 12-pound shot, then graduate to the 16-pound shot used in NCAA, US-ATF, and IAAF competition. In its August 2002 "Stat Corner," the respected athletics periodical Track & Field News proclaimed an"Inverse Relationship Between 12 & 161b Shots":4A look at the accompanying all-time Top 11 lists for high schoolers with the 121b shot-11 because there have been 11 of them over 70 [feet]-and for U.S. men with the 16 sends two messages to aspiring prep putters: If you,re not very good in high school, don't worry about it; few of the big guys were either. If you're great in high school, that may be about as good as you'll ever get. The numbers are astounding. We'll leave it to a technical expert to figure out why ...

Explanation / Answer

Correlation Pearson product-moment correlation = r = ? (xy) / sqrt [ ( ? x2 ) * ( ? y2 ) ] Linear correlation (sample data) = r = [ 1 / (n - 1) ] * ? { [ (xi - x) / sx ] * [ (yi - y) / sy ] } Linear correlation (population data) = ? = [ 1 / N ] * ? { [ (Xi - ?X) / ?x ] * [ (Yi - ?Y) / ?y ] } Simple Linear Regression Simple linear regression line: ? = b0 + b1x Regression coefficient = b1 = ? [ (xi - x) (yi - y) ] / ? [ (xi - x)2] Regression slope intercept = b0 = y - b1 * x Regression coefficient = b1 = r * (sy / sx) Standard error of regression slope = sb1 = sqrt [ ?(yi - ?i)2 / (n - 2) ] / sqrt [ ?(xi - x)2 ] Counting n factorial: n! = n * (n-1) * (n - 2) * . . . * 3 * 2 * 1. By convention, 0! = 1. Permutations of n things, taken r at a time: nPr = n! / (n - r)! Combinations of n things, taken r at a time: nCr = n! / r!(n - r)! = nPr / r! please rate ts as 5...

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