An Economist Wanted to Develop a Multiple Regression Model to Enable

question 57

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & \mathrm { F } \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}\end{array}$$ Test the overall model's validity at the 5% significance level.

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Newborns

Young babies, typically under four weeks old, who are in the very early stages of life outside the womb, characterized by rapid development and high dependency on caregivers.

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A term used to describe individuals who require additional or specialized support due to physical, developmental, behavioral, or emotional considerations.

Physical Growth

The process of bodily changes including increases in height, weight, and muscle mass, typically observed during childhood and adolescence.

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The process of growth or advancement, often involving an improvement in abilities, behaviors, or progress in various aspects of life.