Solve the following problems completely.An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).Draw a scatter diagram of the data.Fit the simple linear regression model using the method of least squares. Find an estimate of σ2.Estimate the mean chloride concentration for a watershed that has 1% roadway area.Find the fitted value corresponding to x = 0.47 and the associated residual.Test the hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure with α = 0.01.Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0%Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%.Plot the residuals versus ŷ and versus x. Interpret these plots.Prepare a normal probability plot of the residuals. Does the normality assumption appear to be satisfied?Determine the correlation coefficient and the coefficient of determination. Solve the following problems completely.An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported theresults of a study on the occurrence of sodium and chloride in surface streams in centralRhode Island. The following data are chloride concentration y (in milligrams per liter) androadway area in the watershed x (in percentage).XyyXy0.194.40.156.60.579.70.7010.60.6710.80.6310.90.4711.80.7012.10.6014.30.7814.70.8115.00.7817.30.6919.21.3023.11.0527.41.0627.71.7431.81.6239.5

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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 7E

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Solve the following problems completely.

An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).

Draw a scatter diagram of the data.
Fit the simple linear regression model using the method of least squares. Find an estimate of σ².
Estimate the mean chloride concentration for a watershed that has 1% roadway area.
Find the fitted value corresponding to x = 0.47 and the associated residual.
Test the hypothesis H₀: β₁ = 0 versus H₁: β₁ ≠ 0 using the analysis of variance procedure with α = 0.01.
Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0%
Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%.
Plot the residuals versus ŷ and versus x. Interpret these plots.
Prepare a normal probability plot of the residuals. Does the normality assumption appear to be satisfied?
Determine the correlation coefficient and the coefficient of determination.