Question

11.6.6 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 following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x in percentage). 4.4 6.6 9.7 10.6 10.8 10.9 11.8 12.1 14.3 14.7 15.0 17.3 19.223.127.4 27.7 31.8 39.5 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 Round your answers to 3 decimal places. Find a 95.00% confidence interval on each of the following: (a) Bo. (b) B. (c) Mean chloride concentration when roadway area x = 0.6%. (d) Find a 95.00% prediction interval on chloride concentration when roadway area x = 0.6%.

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable y Independent Variable: y = 0.47046685 -20.567305 Sample size: 18 R (correlation coefficient) = 0.92312421 R-q=0.85215831 Estimate of error standard deviation: 3.7160731 Parameter estimates: Parameter Estimate Std. Err. DF 95% L. Limit 95% U. Limit Intercept 0.47046685 1.9359134 16 -3.6334863 4.57442 Slope 20.567305 2.1416856 16 16.027134 25.107476 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 1273.5378 1273.5378 92 223872 <0.0001 Error 16 220.94719 13.809199 Total 17 1494.485 Predicted values: X value Pred. Y ..(Pred. y) 95% CI. for meas 954 PI. for bem 0.6 12.81085 0.98083328 (10.731576. 14.890124) (4.6633412, 20.958359)

From above output:

a) (-3.633, 4.574)

b) (16.027, 25.107)

c) (10.732, 14.890)

d) (4.663, 20.958)