Question

The catch basin insert is a device for retrofitting catch basins to improve pollutant removal properties. Consider the following data for one particular type of insert on x- amount filtered (1000s of liters) and y = % total suspended solids removed.

Table 1

x: 23, 45, 68, 91, 114, 205, 228

y: 53, 27, 55, 34, 30, 3, 11

a. Test for a significant relationship using the F test. What is your conclusion? Use α=.05.

b. Show the ANOVA table for these data.

c. Compute the coefficient of determination. Comment on the goodness of fit.

Answer 1

Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel steps are:

Enter the data in excel as:

Click on Data > Data Analysis > Regression > Ok

Input Y range: Select all the data in the Y column including the column name

Input X range: Select all the data in the X column including the column name

Mark the labels

Choose the cell for the output. The excel output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.846411042
R Square	0.716411651
Adjusted R Square	0.659693981
Standard Error	11.34105242
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1624.616936	1624.616936	12.63118979	0.016317416
Residual	5	643.0973498	128.61947
Total	6	2267.714286
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	53.63524317	7.810934725	6.866686902	0.00100143	33.55659626	73.71389009
X	-0.20987946	0.059053794	-3.554038518	0.016317416	-0.361682072	-0.058076849

a. Test for a significant relationship using the F test. What is your conclusion? Use α=.05.

Answer: The F-statistic is 12.631 and the p-value is 0.0163.

Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that there is a significant relationship between the variables.

b. Show the ANOVA table for these data.

Answer:

Source of variation	df	SS	MS	F	Significance F
Regression	1	1624.6169	1624.6169	12.6312	0.0163
Residual	5	643.0973	128.6195
Total	6	2267.7143

c. Compute the coefficient of determination. Comment on the goodness of fit.

Answer: The coefficient of determination is:

.

The value of the coefficient of determination can be interpreted as about 71.64% of the variation in the dependent variable is explained by the regression model. Therefore, this suggests us that the model is the best fit.