a. Estimate a regression model which explains how many viruses a filter removes from the pump as a function of both the thickness of the filter and the filter's manufacturer. Write out this estimated equation to explain how many viruses are removed (use the estimate values and the specific predictors (not 'x1' e.g.)!).

b. Provide the residual plots against each of the two explanatory variables you used in "a" above (thickness and manufacturer). Comment on any irregularities that you notice. If you notice any irregularities in part "b", above, attempt other models which utilize quadratic and/or interaction terms with thickness and manufacturer remaining as explanatory variables.

c. If you find a model with residuals better in line with the regression assumptions, then write out this new, estimated model. Comment on the statistical significance levels of the predictors and provide and comment on the new residual plots for your finalized model.

Viruses	Thickness	Manufacturer X	Manufacturer
3	1	1	X
7	5	1	X
15	5	1	X
33	8	1	X
40	10	1	X
65	12	1	X
67	13	1	X
85	15	1	X
99	17	1	X
130	20	1	X
139	21	1	X
160	23	1	X
7	2	0	Y
8	4	0	Y
12	4	0	Y
22	7	0	Y
54	12	0	Y
68	13	0	Y
78	15	0	Y
87	16	0	Y
100	18	0	Y
120	20	0	Y
133	21	0	Y
140	22	0	Y