An Economist Wanted to Develop a Multiple Regression Model to Enable

question 82

Essay

An economist wanted to develop a multiple regression model to enable him to predict the annual family expenditure on clothes. After some consideration, he developed the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
Where:
y = annual family clothes expenditure (in $1000s) $x _ { 1 }$ = annual household income (in $1000s) $x _ { 2 }$ = number of family members $X _ { 3 }$ = number of children under 10 years of age
The computer output is shown below.
THE REGRESSION EQUATION IS $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$
$\begin{array}{|c|ccc|}\hline \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } \\\hline \text { Constant } & 1.74 & 0.630 & 2.762 \\x_{1} & 0.091 & 0.025 & 3.640 \\x_{2} & 0.93 & 0.290 & 3.207 \\x_{3} & 0.26 & 0.180 & 1.444 \\\hline\end{array}$

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}\hline \text { Source of Variation } & \mathrm{df} & \mathrm{SS} & \mathrm{MS} & \mathrm{F} \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}$
Test at the 1% significance level to determine whether the number of family members and annual family clothes expenditure are linearly related.

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Definitions:

Central Nervous System

The part of the nervous system consisting of the brain and spinal cord, responsible for processing and coordinating information.

Serotonin Dysregulation

A condition wherein the levels, function, or balance of serotonin, a key neurotransmitter in the brain, are abnormal, potentially impacting mood, emotion, and behavior.

Amygdala Dysfunction

Abnormal functioning of the amygdala, a part of the brain involved in emotional processing, which can affect behavior, mood, and responses to stressful stimuli.

Gray Matter

A component of the central nervous system consisting of neuronal cell bodies, dendrites, and unmyelinated axons, crucial for processing information.