An Economist Wanted to Develop a Multiple Regression Model to Enable

question 84

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 $y =$ $$1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 1.74 & 0.630 & 2.762 \\x _ { 1 } & 0.091 & 0.025 & 3.640 \\x _ { 2 } & 0.93 & 0.290 & 3.207 \\x _ { 3 } & 0.26 & 0.180 & 1.444 \\\hline\end{array}$$ S = 2.06 R-Sq = 59.6%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}\end{array}$$ Test the overall model's validity at the 5% significance level.

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Definitions:

Basal Ganglia

Groups of nuclei in the brain associated with a variety of functions, including control of voluntary motor movements, procedural learning, and habits.

Huntington's Disease

A genetic disorder that causes the progressive breakdown of nerve cells in the brain, leading to physical, cognitive, and psychological symptoms.

Cortex

The outer layer of the cerebrum in the brain, involved in complex functions such as thought, perception, and memory.

Classical Conditioning

A teaching approach whereby, through consistent pairing, a response initially elicited by a secondary stimulus is in time elicited by the primary stimulus.