An article in the Journal of Environmental Engineering (Vol. 115, No. 3, 1989, pp. 608–619)…

An article in the Journal of Environmental Engineering (Vol. 115, No. 3, 1989, pp. 608–619) reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The data shown are chloride concentration y (in mg/1) and roadway area in the watershed x (in %).

(a) Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate here?

(b) Fit the simple linear regression model using the method of least squares.

(c) Estimate the mean chloride concentration for a watershed that has 1% roadway area.

(d) Find the fitted value corresponding to x = 0.47 and the associated residual.

(e) Suppose we wish to fit a regression model for which the true regression line passes through the point (0, 0). The appropriate model is  Assume that we have n pairs of data  Show that the least squares estimate of

(f) Use the results of part (e) to fit the model Y = βx + ϵ to the chloride concentration–roadway area data in this exercise. Plot the fitted model on a scatter diagram of the data and comment on the appropriateness of the model.

 

 

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