In: Statistics and Probability
An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp. 608–619) 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). (5px5)
Y: 4.4 6.6 9.7 10.6 10.8 10.9 11.8 12.1 14.3 14.7 15.0 17.3 19.2 23.1 27.4 27.7 31.8 39.5 X: 0.19 0.15 0.57 0.70 0.67 0.63 0.47 0.70 0.60 0.78 0.81 0.78 0.69 1.30 1.05 1.06 1.74 1.62
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. Find an estimate of σ2 .
c) Test the significance of the regression coefficients, use =0.05.
d) Test the adequacy of the regression model, use =0.05.
e) Find the fitted value corresponding to x = 0 47. and the associated residual.