The rgression equation is WEIGHT = -288-.83 HEADLEN + 0.53 LENGTH + 11.7 CHEST P

Question

The rgression equation is WEIGHT = -288-.83 HEADLEN + 0.53 LENGTH + 11.7 CHEST Predictior            Coef         SECoef                     T                        P Constant               -288         37.93                     -7.59               0.000 HEADLEN           -0.83         5.668                     -0.15               0.884 LENGTH               0.53          1.183                     0.45                 0.672 CHEST                  11.7           1.109                  10.55               0.000         A bear is found to have a head length of 15.0 in, a length of66.0 in, and a chest size of 59.0 in. What is the predicted weight ofthe bear?     The rgression equation is WEIGHT = -288-.83 HEADLEN + 0.53 LENGTH + 11.7 CHEST Predictior            Coef         SECoef                     T                        P Constant               -288         37.93                     -7.59               0.000 HEADLEN           -0.83         5.668                     -0.15               0.884 LENGTH               0.53          1.183                     0.45                 0.672 CHEST                  11.7           1.109                  10.55               0.000         A bear is found to have a head length of 15.0 in, a length of66.0 in, and a chest size of 59.0 in. What is the predicted weight ofthe bear?    

Explanation / Answer

A regression comes up with the "best guess" from the data ofthe values of the COEFFICIENTS in the regression equation. The coefficients are the things we multiply the independentvariables (the Xs, or the things on the right-hand-side) by to getour best guess of the predicted value of the dependent variable(the Y, or the thing on the left-hand-side). . EXAMPLE: Suppose we regress test scores on hours of studying and hoursof sleep the night before the exam. Our regression equationwould be Score = b0 + b1*Hours_Studying + b2*Hours_Sleep . The variable Score is our dependent variable; the variablesHours_Studying and Hours_Sleep are our independent variables; andthe numbers b0, b1, and b2 are our COEFFICIENTS. . The regression equation tells us our best guess as to therelationship between our test scores and our hours of studying andhours of sleeping. . We use the data to make our best guesses about the values ofb0, b1, and b2. These coefficients can do four things forus: 1) We can do statistical tests on the relationships betweenthe variables (that's what the T and P columns are doing, testingthe hypothesis that the independent variable in that row has noeffect on WEIGHT); . 2) We get a sign (positive or negative), that tells us whetheran increase in hours studying is predicted to increase our score ordecrease our score (curiously, in your problem, bigger headspredict a lower weight, but, if you know how to read the T or Pcolumns, you can see that the coefficient is not statisticallysignificantly different from 0, so there's no point trying tointerpret it; if that doesn't make sense to you now, it probablywill soon); . 3) We get a magnitude of the effect. b1 tells us BY HOWMANY UNITS we expect our score to go up if we increase hours ofstudying by 1 hour. If b1=4, then we predict that if youspend 2 more hours studying, you'll increase your score by 8points. (Because Hours_Sleep is also in the regression, ourcoefficient on Hours_Studying tells us the effect of studying onscores, holding sleep constant. So we're getting the extra 2hours of studying by skipping some gamebox time, not by staying uplater.) . 4) The use that's relevant for this problem: we can plugin specific values of our independent variables to make a "bestguess" prediction of our dependent variable. . So if b0 = 20, b1 = 4, and b2 = 2, our regressionequation in the example would be SCORE = 20 + 4*Hours_Studying + 2*Hours_Sleeping. . If I tell you that a student spent 20 hours studying and 8hours sleeping, you can predict her score will be SCORE = 20 + 4*20 + 2*8 = 20 + 80 + 16 = 116. . Similarly, in your problem, you can make a best guess about abear's weight once you know the values of the othervariables. Just plug the values they give you into theequation: . WEIGHT = -288 -0.83*15 + 0.53*66 + 11.7*59 and multiply it out.

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