Question

My Notes Ask Your Teacher 2. -15 points DevoreStat9 12.E.075 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, Σ(speed) = 205.5, Σ(speed). 3881.08, Σ(rate): 35.15, Σ(rate)2-112.661, and Σ(speed)(rate) = 660.150. | (a) Calculate the equation of the least squares line that you would use to predict stride rate from speed. (Round al 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). 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. Need Help?Read It Talk to a Tutor

Answer 1

Ans:

a)

slope,b=(11*660.15-205.5*35.15)/(11*3881.08-205.5^2)=0.0830

intercept=(35.15-0.08302*205.5)/11=1.6445

y'=0.0830x+1.6445

where x=speed, y =rate

b)

slope,b=(11*660.15-205.5*35.15)/(11*112.661-35.15^2)=10.2241

intercept=(205.5-10.22409*35.15)/11=-13.9888

y'=10.2241x-13.9888

where x=rate,y=speed

c)

For a,

r=(11*660.15-205.5*35.15)/SQRT((11*3881.08-205.5^2)*(11*112.661-35.15^2))=0.9213

R^2=0.9213^2=0.849

For b,

r=(11*660.15-205.5*35.15)/SQRT((11*112.661-35.15^2)*(11*3881.08-205.5^2))=0.9213

R^2=0.9213^2=0.849

d)Both are same.