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:

Inelastic

A characteristic of goods whose demand does not change significantly when the price of the good changes.

Prices

The amount of money required to purchase goods or services, often determined by factors such as supply and demand.

Maximizing Utility

The process by which individuals allocate their resources to obtain the highest possible satisfaction from their consumption.

Marginal Utility

The change in satisfaction or usefulness obtained by consuming one additional unit of a good or service.