s 1 - 10 refer to the following. Over the past 30 years, public awareness and concern about air pollution

Questions 1 - 10 refer to the following.

Over the past 30 years, public awareness and concern about air pollution have escalated dramatically. Venturi scrubbers have been used for the removal of submicron particulate matter found in dust, fogs, fumes, odors, and smoke from gas streams. An experiment was conducted to determine the effect of air flow rate, water flow rate (liters/minute), the recirculating water flow rate (liters/minute), and the orifice size (mm) in the air side of the pneumatic nozzle on the performance of the scrubber as measured by the number of transfer units (NTU). The results are given below.

Air flow	Water flow	Recirc. Water flow	Orifice diameter	NTU
2.475	5.7	18.9	2.45	1.93
2.475	5.7	18.9	2.45	1.95
1.484	5.7	37.9	1.3	1.16
1.484	5.7	37.9	1.3	1.17
1.294	5.7	37.9	2.45	1.1
1.294	5.7	37.9	2.45	1.04
1.286	5.7	18.9	1.3	0.98
1.286	5.7	18.9	1.3	0.99
2.475	7.6	37.9	2.45	2.01
2.475	7.6	37.9	2.45	2.04
1.295	7.6	18.9	1.3	1.29
1.295	7.6	18.9	1.3	1.25
1.286	7.6	37.9	1.3	1.24
1.286	7.6	37.9	1.3	1.09
1.274	7.6	18.9	2.45	1.11
1.274	7.6	18.9	2.45	1.14
0.665	1.9	18.9	0.8	0.65
0.665	1.9	18.9	0.8	0.72

Assuming linear relationship, run a regression for the data, and then state the estimated regression equation.
State the value of the coefficient of determination and then interpret it.

3. Print out the matrices (X’X) ^-1 , (X’Y) , and the variance-covariance matrix V(b) . Use these results to compute the standard errors of each of the regression coefficients.

4. At the 5% level of significance, use individual t tests to determine which independent variables will be kept in the model, and which will be omitted. Explain.

5. Interpret the coefficient b ₂ , where x ₂ is the water flow variable.

6. Construct a 90% confidence interval for ${{\beta }_{2}}$

7. Perform an F-test to determine if the variables water flow, recirculating water flow, and orifice size, taken as a group, have any linear explanatory power.

8. One of the engineers believes that the variance of the error terms might be directly proportional to the squares of the expected values of the number of transfer units, given the values of the x variables. If so, what is this called and what assumption would be violated? Using the full regression model with all of the x variables still included, test to see if this assumption is violated. Show each step of the test. Based on your results, does a correction procedure need to be done?

9. Based on your results in questions 4, 7, and 8, run an appropriately revised regression equation.

10. Another consultant suggested that the model’s form should be log-linear. Estimate a log- linear model using all of the x variables, and interpret the coefficient b ₂ . Then, type the original (multiplicative) model prediction equation that would produce the estimated log-linear form.

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