The Simple Linear Regression Model Provides a Very Good Fit $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$

question 95

Essay

The simple linear regression model provides a very good fit to a data set on rainfall and runoff volume. The equation of the least squares line is $\hat { y } = - 1.128 + .82697 X , Y^ { 2 } = .975 , \text { and } s = 5.24$
a. Use the fact that $s _ { y } = 1.44$
when rainfall volume is 40 m $3$
to predict runoff in a way that conveys information about reliability and precision. Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning.
b. Calculate a PI for runoff when rainfall is 50 using the same prediction level as in part (a). What can be said about the simultaneous prediction level for the two intervals you have calculated?

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Definitions:

Marginal Cost

Marginal cost refers to the increase or decrease in the total cost when the quantity produced is incremented by one unit.

Fixed Cost

Costs that remain constant regardless of the amount of goods produced or sold, including rent, wages, and insurance premiums.

Sunk Cost

Costs that have already been incurred and cannot be recovered or refunded, and should not influence future business decisions.

Average Fixed Cost

The cost incurred for fixed inputs (rent, salaries) divided by the quantity of output produced, which decreases as production increases.