Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σx = 63.8; Σx2 = 520.96; Σy = 89.8; Σy2 = 1046.96; Σxy = 731.35 x 6.2 8.7 7.0 7.5 8.1 6.9 10.0 9.4 y 9.7 10.8 10.5 11.3 14.2 7.0 14.1 12.2 (a) Find the equation of the least-squares line. (Round your answers to three decimal places.) ŷ = + x (c) Find the sample correlation coefficient r and the sample coefficient of determination r2. (Round your answers to three decimal places.) r = r2 = Explain the meaning of r2 in the context of the application. (Round your answer to one decimal place.) % of the variance in blood glucose leve
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information.
| x | 6.2 | 8.7 | 7.0 | 7.5 | 8.1 | 6.9 | 10.0 | 9.4 |
| y | 9.7 | 10.8 | 10.5 | 11.3 | 14.2 | 7.0 | 14.1 | 12.2 |
ŷ = + x
| r = | |
| r2 = |
Explain the meaning of
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