1. Let z be the rainfall volume (m³) and y be the runoff volume (m³) for a particular location: x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 4 10 13 15 15 25 27 46 38 46 53 70 82 99 100 y The summary statistics for n = 15 data points are = 53.2 and SD = 38.347 and y = 42.867 and SD, 32.111, and r = 0.9876 (a) Calculate point estimates of the slope and intercept of the population regression line and their associated standard errors? What is the estimate of the noise o? (b) Predict the runoff volume at z* = 70 and its associated 95%-predictive interval. (c) Among * 70, approximately how many percents of them will have a runoff volume more than 42.867?
1. Let z be the rainfall volume (m³) and y be the runoff volume (m³) for a particular location: x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 4 10 13 15 15 25 27 46 38 46 53 70 82 99 100 y The summary statistics for n = 15 data points are = 53.2 and SD = 38.347 and y = 42.867 and SD, 32.111, and r = 0.9876 (a) Calculate point estimates of the slope and intercept of the population regression line and their associated standard errors? What is the estimate of the noise o? (b) Predict the runoff volume at z* = 70 and its associated 95%-predictive interval. (c) Among * 70, approximately how many percents of them will have a runoff volume more than 42.867?
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Transcribed Image Text:1. Let z be the rainfall volume (m³) and y be the runoff volume (m³) for a particular location:
x
5 12 14 17 23 30 40 47 55 67 72 81 96 112 127
y
4 10 13 15 15 25 27 46 38 46 53 70 82 99 100
The summary statistics for n = 15 data points are = 53.2 and SD = 38.347 and y = 42.867 and
SD, 32.111, and r = 0.9876
(a) Calculate point estimates of the slope and intercept of the population regression line and their
associated standard errors? What is the estimate of the noise σ?
(b) Predict the runoff volume at z* = 70 and its associated 95%-predictive interval.
(c) Among * 70, approximately how many percents of them will have a runoff volume more than
42.867?
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