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:

Least-squares Regression

A statistical method used to determine the best-fitting line through a set of points by minimizing the sum of the squares of the offsets.

Squared Deviations

The squared differences between each data point in a set and the mean of that set, used in statistical analysis to measure variance.

Contribution Margin

The amount remaining from sales revenue after variable costs are subtracted, showing what's left over to cover fixed costs and generate profit.

Sales Volume

This refers to the total number of units of a product or service sold over a specific period.