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

question 26

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 $x _ { 2 }$ is negatively linearly related to y?

---

Definitions:

Size

The overall dimensions or magnitude of an object, person, or concept.

Reciprocity of Liking

The tendency for individuals to like others who express liking towards them, playing a significant role in the development of friendships and romantic relationships.

Different

Not the same as another or each other; unlike in nature, form, or quality.

Rich

Having an abundance of wealth, resources, or valuable possessions.