A First-Order Model Was Used in a Regression Analysis Involving $x _ { 1 }$

question 95

Essay

A first-order model was used in a regression analysis involving 25 observations to study the relationship between a dependent variable y and three independent variables, $x _ { 1 }$ , $x _ { 2 }$ and $x _ { 3 }$ . The analysis showed that the mean squares for regression is 160 and the sum of squares for error is 1050. In addition, the following is a partial computer printout. $$\begin{array} { | c | c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } \\\hline \text { Constant } & 25 & 4 \\x _ { 1 } & 18 & 6 \\x _ { 2 } & - 12 & 4.8 \\x _ { 3 } & 6 & 5 \\\hline\end{array}$$ Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the value of y?

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Definitions:

Operating Assets

Assets used by a business in its operational activities to generate revenue, excluding investments and non-operating assets.

Residual Income

The income that exceeds the minimum required return on investment or capital; often used in performance measurement and evaluation.

Minimum Required Rate

The lowest return on investment that a company or individual deems acceptable, often used in financial analysis and capital budgeting.

Operating Assets

Operating assets are the assets a company uses in its daily operations to generate revenue, such as inventory, property, plant, and equipment.