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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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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?
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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