My Notes Ask Your 12 E.075 An investigation was carried out to study the relatio

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My Notes Ask Your 12 E.075 An investigation was carried out to study the relationship between speed (t/sec) and stride rate (number of steps taken/sec) among female marathon runners n-11, 2tspeed). 2054, Zspeed), 3886.08, ?(rate)-35. 12, ?(rate), 1 12.661, and ?(speed)( rate)-650. 132. Resulting summary quantaies inclu (e) Calculate the equation of the least squares lire that you would use to predict stride rate from speed. (Round all numerical numerical values to four decimal places.) (b) Calculate the equation of the least squares line that you would use to predict speed from stride rate (ound all (e) Calculate the coefficient of determination for the regression of stride rate on speed of pert (a) and for the regression of speed on stride rate of part (b). (Round your answers to decimal places) for part (a) for part (b) How are these related? The coefficient of determination is much larget for part (a). The coefficient of determination is much larger for part (b). The coefficients of determination for (a) and (b) are the same or very similar Need Help? Lese Teh to Ter

Explanation / Answer

Let Speed be X and Stride Rate be Y

For X:

Mean, X bar = Sum of Speed/n = 205.4/11 = 18.67

SSx= Speed^2 - (Mean X)^2/n = 3886.08 - (18.67^2)/11 = 3854.39

Var X = SS/n-1 = 3854.39/10 = 38.54

For Stride Rate:

For Y:

Mean, Y bar = Sum of Stride Rate/n = 35.12/11 = 3.19

SSy= Stride^2 - (Mean Y)^2/n = 112.661 - (3.19^2)/11 = 111.73

Var Y = SS/n-1 = 111.73/10 = 1.12

E(XY) = 6.45

Cov (X,Y) = E(XY)-E(X)*E(Y)= 660.132/10 - 18.67*3.19= 6.45

a)

b0 = Mean Y - b1*Mean X

b1 = cov (XY)/var(X) = 6.45/38.54 = 0.167

b0 = 3.19 - 18.67*0.167 = 0.072

Regression eqn Y = 0.072+0.167X

b) The other way round with variables interchanged

b1 = 6.45/1.12 = 5.75

b0 = 18.67 - 3.19*5.75 = 0.3275

X = 0.3275 + 5.75 Y

C) The coefficient of correlation will be the same in either case

r = cov(xy)/sx*sy = 6.45/sqrt(38.54*1.12) = 0.98

Let me know if you need anything else, if not please don't forget to like the answer :)

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