# Lesson 205 number 1 essay question the data below

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Lesson 205Number 1(Essay Question)The data below were gathered on a random sample of 5 basking sharks,swimming through the water and filter-feeding, i.e. letting the waterbring food into their mouths.BodyLength(meters)Mean Speed(meters/seconds)40.894.50.8340.766.50.945.50.94a) What is the value of the correlation coefficient for these data?b) Find the equation of the least squares line describing the relationshipbetween x = body length and y = mean speed.Number 2(Essay Question)One measure of form for a runner is stride rate, defined as the numberof steps per second. A runner is considered to be efficient if the striderate is close to optimum. The stride rate is related to speed; the greaterthe speed, the greater the stride rate. In a study of 21 top femalerunners, researchers measured the stride rate for different speeds. Thefollowing table gives the average stride rate of these women versus thespeed.
(Data is from R.C. Nelson, C.M. Brooks, and N.L. Pike, “Biomechanicalcomparison of male and female runners”, in P. Milvy (ed.), TheMarathon: Physiological, Medical, Epistemological, and PsychologicalStudies, New York Academy of Sciences, 1977, pp. 793-807.)Speed15.86 16.88 17.5 18.62 19.97 21.06 22.11StrideRate3.083.123.17 3.253.363.463.55a) Plot the data on a scatterplot. Describe any patterns (or lack thereof)in the data.b) Find the equation of the least squares regression line.

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