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, sigma(speed) = 205.1, sigma(speed)^2 = 3886.08, sigma(rate) = 35.11, sigma(rate)^2 = 112.611, and sigma(speed)(rate) = 660.124. 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.) 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.) 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 (Round all numerical values to four decimal places.) for part (a) 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 coefficient of determination for (a) and (b) are the same or very similar.
a) mean of speed= 205.1 / 11 = 18.64545.....mean of rate = 35.11/11 = 3.19182......
variance of speed = 3886.08 - ( 205.1)^2 /11 = 61.89727.....
variacne of rate = 112.611 - (35.11)^2 /11 = 0.5462636......
covariance(speed,rate) = 660.124 - ( 205.1 * 35.11) / 11 = 5.482091......
a) m = 5.482091 / 0.5462636 = 10.03561......
b = 18.64545 - ( 10.03561 * 3.19182 ) = -13.38643......
so, equation : Y-hat = 10.03561* X-hat - 13.38643
b) m = 5.482091 / 61.89727 = 0.08856757........
b = 3.19182 - ( 0.08856757 * 18.64545 ) = 1.540438........
so, equation : X-hat = 0.08856757* Y-hat + 1.540438........
c) a)coeff. of determinant = 5.482091^2 / ( 61.89727 * 0.5462636 ) = 0.88883.....
b) coeff. of determinant = 0.88883......
The coeffiecients of determination for (a) and (b) are the same
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