When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the pressure drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): 1 2 3 4 6 7 8 9 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 (a) Fit the least square regression equation to predict the flux (flow per area) through the pressure drop across a membrane. (b) Find the estimated flux when the pressure drop across a membrane is 4.50. (c) Calculate the coefficient of correlation. Interpret your result.
When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the pressure drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): 1 2 3 4 6 7 8 9 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 (a) Fit the least square regression equation to predict the flux (flow per area) through the pressure drop across a membrane. (b) Find the estimated flux when the pressure drop across a membrane is 4.50. (c) Calculate the coefficient of correlation. Interpret your result.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Transcribed Image Text:When purifying drinking water you can use a so-called membrane filtration. In an
experiment one wishes to examine the relationship between the pressure drop across a
membrane and the flux (flow per area) through the membrane. We observe the
following 10 related values of pressure (x) and flux (y):
1
2
3
4
5
7
8.
9
10
Pressure (x)
1.02
2.08
2.89
4.01
5.32
5.83
7.26
7.96 | 9.11
9.99
Flux (y)
1.15
0.85
1.56
1.72
4.32
5.07
5.00
5.31
6.17
7.04
(a) Fit the least square regression equation to predict the flux (flow per area) through
the
pressure drop across a membrane.
(b) Find the estimated flux when the pressure drop across a membrane is 4.50.
(c) Calculate the coefficient of correlation. Interpret your result.
(d) Given Sxx = 83.25961 and Se = 0.64460653. Test, at the 0.01 level of significance,
whether there is linear relationship between the pressure drop across a membrane and the flux
(flow per area) through the membrane.
(e) Construct a 98% confidence interval for the mean flux for the pressure drop across a
membrane is 4.5.
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