Question

The catch basin in a storm-sewer system is the interface between surface runoff and the sewer. The catch-basin insert is a device for retrofitting catch basins to improve pollutantremoval properties. The article "An Evaluation of the Urban Stormwater Pollutant Removal Efficiency of Catch Basin Inserts” (Water Envir. Res., 2005: 500–510) reported on tests of various inserts under controlled conditions for which inflow is close to what can be expected in the field. Consider the following data, read from a graph in the article, for one particular type of insert on x = amount filtered (1000s of liters) and y = % total suspended solids removed. x 23 45 68 91 114 136 159 182 205 228 y 53.3 26.9 54.8 33.8 29.9 8.2 17.2 12.2 3.2 11.1 Summary quantities are Ex; = 1251, Ex} = 199,365, Ey; = 250.6, y= 9249.36, 2x;y; = 21,904.4 a. Does a scatter plot support the choice of the simple linear regression model? Explain. b. Obtain the equation of the least squares line. c. What proportion of observed variation in % removed can be attributed to the model relationship? d. Does the simple linear regression model specify a useful relationship? Carry out an appropriate test of hypotheses using a significance level of .05. e. Is there str concluding that there is at least a 2% decrease in true average suspended solid removal associated with a 10,000 liter increase in the amount filtered? Test appropriate hypotheses using a = .05.

Answer 1

a)

50 100 150 200 250

yes

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8372
R Square	0.7010
Adjusted R Square	0.6636
Standard Error	10.5350
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2081.4348	2081.4348	18.7540	0.0025
Residual	8	887.8892	110.9862
Total	9	2969.3240
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	52.6269	7.1847	7.3249	0.0001	36.0590	69.1948
x	-0.2204	0.0509	-4.3306	0.0025	-0.3377	-0.1030

y^ = 52.6269 - 0.2204 *x

c)

R^2 = 0.701

hence 70.1% of variation

d)

p-value of F-test is 0.0025< alpha

hence we reject the null hypothesis

the model is significant