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:

Index Funds

A type of mutual fund or exchange-traded fund designed to follow or track the components of a market index, such as the S&P 500.

PHStat

A software add-in for Microsoft Excel that assists in statistical analyses.

Variance

A measure of the dispersion or spread of a set of values, calculated as the average of the squared deviations from the mean of the set.

Index Funds

Mutual funds or exchange-traded funds (ETFs) designed to follow certain preset rules so that the fund can track a specified basket of underlying investments.