Question

ASK YOUR TEACHER An investigation was carried out to study the relationship between speed (ft/sec) and striderate number of steps taken/sec) among female marathon runners. Resulting summary quantities included n = 11 speed) = 2052, (speed) - 1881.00, rate) - 35.13. Brate)? - 112.671, and speed)(rate) - 660.118 (a) Calculate the equation of the least squares line that you would use to predict striderate from speed (Round il numerical values to four decimal places) - 0.08998x + 1.5152 (1) Calculate the equation of the least squares line that you would use to predict speed from striderate (Hound all numerical values to four decimal places) - 9.996-Ax - 13.2703 (c) Calculate the coefficient of determination for the regression of striderate on speed of part (a) and for the regression of speed on stride rate of part() (Round your answers to three decimal places) for part(a) 09068 for part (b) How are these related? The coefficient of determination is much larger 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

Answer 1

a) if x = speed and y = rate

Ʃx =	205.2
Ʃy =	35.13
Ʃxy =	660.118
Ʃx² =	3881.08
Ʃy² =	112.671
Sample size, n =	11
x̅ = Ʃx/n = 205.2/11 =	18.654545
y̅ = Ʃy/n = 35.13/11 =	3.1936364
SSxx = Ʃx² - (Ʃx)²/n = 3881.08 - (205.2)²/11 =	53.167273
SSyy = Ʃy² - (Ʃy)²/n = 112.671 - (35.13)²/11 =	0.4785545
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 660.118 - (205.2)(35.13)/11 =	4.7838182

Slope, b = SSxy/SSxx = 4.78382/53.16727 = 0.0899767

y-intercept, a = y̅ -b* x̅ = 3.19364 - (0.08998)*18.65455 = 1.5151611

Regression equation :

ŷ = (0.0900) x + 1.5152

b)

if x = rate and y = speed

Ʃx =	35.13
Ʃy =	205.2
Ʃxy =	660.118
Ʃx² =	112.671
Ʃy² =	3881.08
Sample size, n =	11
x̅ = Ʃx/n = 35.13/11 =	3.1936364
y̅ = Ʃy/n = 205.2/11 =	18.654545
SSxx = Ʃx² - (Ʃx)²/n = 112.671 - (35.13)²/11 =	0.4785545
SSyy = Ʃy² - (Ʃy)²/n = 3881.08 - (205.2)²/11 =	53.167273
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 660.118 - (35.13)(205.2)/11 =	4.7838182

Slope, b = SSxy/SSxx = 4.78382/0.47855 = 9.9963906

y-intercept, a = y̅ -b* x̅ = 18.65455 - (9.99639)*3.19364 = -13.270291

Regression equation :

ŷ = (9.9964) x -13.2703

c)

For part a) :

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = (4.78382)²/(53.16727*0.47855) = 0.899

For part b) :

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = (4.78382)²/(0.47855*53.16727) = 0.899

The Coefficient of determination for a) and b) are the same or very similar