An investigation was carried out to study the relationship between speed (ft/sec

Question

An investigation was carried out to study the relationship between speed (ft/sec) and stride rate (number of steps taken/sec) among female marathon runners. Resulting summary quantities included n = 11, (speed) 205.3 (speed)2 = 3884.08, (rate) = 35.12, (rate)2-112.641, and (speed)(rate) = 660.120. (a) Calculate the equation of the least squares line that you would use to predict stride rate from speed. (Round all 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. (Round all numerical values to four decimal places.) (c) Calculate the coefficient of determination for the regression of stride rate on speed of part (a) and for the regression of speed on stride rate of part (b). (Round your answers to three decimal places.) for part (a) for part (b) How are these related? O The coefficient of determination is much larger for part (a) O The coefficient of determination is much larger for part (b) O The coefficients of determination for (a) and (b) are the same or very similar.

Explanation / Answer

a) here SSrate =112.641-35.122/11=0.5124

and SSspeed =3884.08-205.32/11=52.4355

SSp=660.120-35.12*205.3/11=4.6531

hence slope =SSp/(SSspped)1/2=0.6426

and intercept =(!/11)*(35.12-0.6426*205.3)=-8.8002

hence equation :Yhat =-8.8002+4.6531*X

b) similarly as above:

Yhat =-2.0899+6.5002*X

c) Coefficient of determiantion for part (A) =SSp2/(SSspped *SSrate) =0.8058

Coefficient of determiantion for part (B) =SSp2/(SSspped *SSrate) =0.8058

the Coefficient of determiantion for a abd b are the same or very similar

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