Inference from a Fitted Least Squares Simple Regression Model Exercise 1 Reconsider the relationship between city air particulate and rates of childhood asthma first discussed in HWK 10. We sample 15 cities for particulate measured in parts-per-million (ppm) of large particulate matter and for the rate of childhood asthma measured in percents. The data are as follows: variable particulate (x) 11.6 15.9 15.7 7.9 6.3 13.7 13.1 10.8 6.0 7.6 14.8 7.4 16.2 13.1 11.2 asthma % (y) 14.5 16.6 16.5 12.6 12.0 15.8 15.1 14.2 12.2 13.1 16.0 12.9 16.4 15.4 14.4 variable: size mean variance particulate 15 11.42 13.05029 asthma 15 14.51333 2.635524 a. Suppose we sample a new city whose particulate is 13 ppm. If reasonable, create a 95% interval for the predicted rate of childhood asthma in this city. If not reasonable, explain why. b. Create a 95% confidence interval for the average rate of childhood asthma among cities with 10 ppm of large particulate. Is this confidence interval wider or narrower than a 95% prediction interval for the rate of childhood asthma in the next city with 10 ppm of large particulate? Explain why this relationship makes sense. c. If reasonable, create a 95% interval for the predicted rate of childhood asthma in the next city sampled that has 3 ppm of large particulate. If not reasonable, explain why.
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Variable Particulate: 11.6, 15.9, 15.7, 7.9, 6.3, 13.7, 13.1, 10.8, 6.0, 7.6, 14.8, 7.4, 16.2 Variable Asthma: 14.5, 16.6, 16.5 Show more…
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