Below You Are Given a Partial Computer Output Based on a Sample

question 26

Essay

Below you are given a partial computer output based on a sample of 8 observations, relating an independent variable x) and a dependent variable y).
$$\begin{array}{l}\begin{array} { l c c } & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 13.251 & 10.77 \\\mathrm { X } & 0.803 & 0.385\end{array}\\\\\text { Analysis of Variance }\\\begin{array} { l c } \text { SOURCE } & \text { SS } \\\text { Regression } & \\\text { Error Residual) } & 41.674 \\\text { Total } & 71.875\end{array}\end{array}$$
a. Develop the estimated regression line.
b. At α = 0.05, test for the significance of the slope.
c. At α = 0.05, perform an F test.
d. Determine the coefficient of determination.

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Definitions:

Economic Profit

Economic profit is the difference between total revenue and total costs, including both explicit and implicit costs, measuring the profit that exceeds the next best alternative use of resources.

Short Run

A period in economics during which at least one input is fixed and cannot be changed, limiting the ability of a firm to adjust to market changes.

Fixed Inputs

Resources used in the production process whose quantity cannot easily be changed in the short run, such as buildings and machinery.

Marginal Product

The additional output that is produced by adding one more unit of a specific input, ceteris paribus (with all other inputs held constant).