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vodka [1.7K]
3 years ago
7

An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate ma

tter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot

Mathematics
1 answer:
kramer3 years ago
4 0

Answer:

If the model is appropiate, the residual of a linear regression model, when plotted in a scatter plot (residuals vs. independent variable), should be spread around 0, with no significant slope (slope = 0).

Step-by-step explanation:

The residual is defined as the difference between the observed and the predicted value.

If the model is appropiate, the residual of a linear regression model, when plotted in a scatter plot (residuals vs. independent variable), should be spread around 0, with no significant slope (slope = 0).

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Answer:

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b) The exact method consists in the application of the First and Second Derivative Tests. First and second derivatives are, respectively:

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The First Derivative Test consists in equalizing the first derivative to zero and solving the expression:

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The exact solution is P(x,y) = (0.07,1.04), indicating that graphic solution leads to a good approximation.

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Step-by-step explanation:

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Now we get,

FV=(4500)(\frac{(1+\frac{0.06}{1})^{1\times10})-1}{\frac{0.06}{1}})\\\\\Rightarrow\ FV=(4500)(\frac{(1.06)^{10})-1}{0.06})\\\\\Rightarrow\ FV=(4500)(\frac{0.79084769654}{0.06})\\\\\Rightarrow\ FV=(4500)(13.1807949423)\\\\\Rightarrow\ FV=59313.5772407\approx59313.58 \ \

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Step-by-step explanation:

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