Doctors are interested in the relationship between the dosage of a medicine and the time required for a patient’s recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours). These patients have similar characteristics except for medicine dosages. Dosage level 1.2 1.3 1.0 1.4 1.5 1.8 1.2 1.3 1.4 1.3 Recovery time 25 28 40 38 10 9 27 30 16 18 a. Estimate the linear regression of recovery time on dosage level. b. Find and interpret a 90% confidence interval for the slope of the population regression line. c. Would the sample regression derived in part a be useful in predicting recovery time for a patient given 2.5 grams of this drug? Explain your answer.
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!
Doctors are interested in the relationship between the dosage of a medicine and the time required for a patient’s recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours). These patients have similar characteristics except for medicine dosages.
Dosage level 1.2 1.3 1.0 1.4 1.5 1.8 1.2 1.3 1.4 1.3
Recovery time 25 28 40 38 10 9 27 30 16 18
a. Estimate the linear regression of recovery time on dosage level.
b. Find and interpret a 90% confidence interval for the slope of the population regression line.
c. Would the sample regression derived in part a be useful in predicting recovery time for a patient given 2.5 grams of this drug? Explain your answer.
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