An Economist Wanted to Develop a Multiple Regression Model to Enable

question 37

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
ŷ = $1.74 + 0.091 x _ { 1 } + 0.93 x _ { 2 } + 0.26 x _ { 3 }$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 1.74 & 0.630 & 2.762 \\x _ { 1 } & 0.091 & 0.025 & 3.640 \\x _ { 2 } & 0.93 & 0.290 & 3.207 \\x _ { 3 } & 0.26 & 0.180 & 1.444 \\\hline\end{array}$$ se = 2.06, R2 = 59.6%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}\end{array}$$ Test the overall model's validity at the 5% significance level.

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Definitions:

Consumption Sector

A segment of the economy that involves individuals and households that use goods and services for personal needs rather than for manufacturing or resale.

Direct

Direct refers to an immediate or straightforward method or approach, without involving intermediaries or detours.

Progressive

Supporting or advocating for gradual social, political, or economic reform through governmental action.

Federal Personal Income Tax

The tax levied by the federal government on individuals' income, including wages, investments, and other forms of earnings.