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

question 34

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. $$\begin{array} { | c | c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } \\\hline \text { Constant } & 25 & 4 \\x _ { 1 } & 18 & 6 \\x _ { 2 } & - 12 & 4.8 \\x _ { 3 } & 6 & 5 \\\hline\end{array}$$ Test at the 5% significance level to determine whether $x _ { 1 }$ is linearly related to y.

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Definitions:

Thirsty

The feeling of needing to drink liquids, often as a result of dehydration or the desire for refreshment.

External Cues

External signals or triggers that influence behavior or responses.

Obesity

A medical condition characterized by excessive body fat that presents a risk to health, typically measured by a body mass index (BMI) of 30 or higher.

Homeostasis

The tendency of a biological system to maintain stability or equilibrium within its internal environment when dealing with external changes.