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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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.
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