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

question 25

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 sufficient evidence at the 5% significance level to indicate that $X _ { 3 }$ is positively linearly related to y?

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Definitions:

Acts Aggressively

Engaging in behaviors intended to harm or intimidate others.

Personality Disorders

A group of mental disorders characterized by enduring maladaptive patterns of behavior, cognition, and inner experience, exhibited across many contexts and deviating from those accepted by the individual's culture.

Axis I Disorders

Refers to clinical conditions that can be the primary focus of clinical attention, including depression, anxiety disorders, and schizophrenia, among others.

Paranoid Personality Disorder

A mental health condition characterized by pervasive distrust and suspicion of others' motives without adequate basis.