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1. Suppose the variables x = commuting distance and y = comuting time are related according to the simple linear regression model with σ = 10. a. If n = 5 observations are made at the x values x₁ = 5, x₂ = 10, x₂ = 15, x₁ = 20, and x₂ = 25, calculate the standard deviations of the five corresponding residuals. b. Repeat part (a) for x, = 5, x, = 10, x₂ = 15, x₁ and x5 = 50. c. What do the results of parts (a) and (b) imply al the deviation of the estimated line from the obse tion made at the largest sampled x value?

1. Suppose the variables x = commuting distance and y = comuting time are related according to the simple linear regression model with σ = 10. a. If n = 5 observations are made at the x values x₁ = 5, x₂ = 10, x₂ = 15, x₁ = 20, and x₂ = 25, calculate the standard deviations of the five corresponding residuals. b. Repeat part (a) for x, = 5, x, = 10, x₂ = 15, x₁ and x5 = 50. c. What do the results of parts (a) and (b) imply al the deviation of the estimated line from the obse tion made at the largest sampled x value?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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1. Suppose the variables x = commuting distance and y = comuting time are related according to the simple linear regression model with σ = 10. a. If n = 5 observations are made at the x values x₁ = 5, x₂ = 10, x₂ = 15, x₁ = 20, and x, = 25, calculate the standard deviations of the five corresponding residuals. b. Repeat part (a) for x, = 5, x, = 10, x² = 15, xâ = 20, and x = 50. c. What do the results of parts (a) and (b) imply about the deviation of the estimated line from the observa- tion made at the largest sampled x value?
Transcribed Image Text:1. Suppose the variables x = commuting distance and y = comuting time are related according to the simple linear regression model with σ = 10. a. If n = 5 observations are made at the x values x₁ = 5, x₂ = 10, x₂ = 15, x₁ = 20, and x, = 25, calculate the standard deviations of the five corresponding residuals. b. Repeat part (a) for x, = 5, x, = 10, x² = 15, xâ = 20, and x = 50. c. What do the results of parts (a) and (b) imply about the deviation of the estimated line from the observa- tion made at the largest sampled x value?
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