An Economist Wanted to Develop a Multiple Regression Model to Enable

question 12

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 $y=1.74+0.091 x_{1}+0.93 x_{2}+0.26 x_{3}$
$\begin{array}{|c|ccc|}\hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm{T} \\\hline \text { Constant } & 1.74 & 0.630 & 2.762 \\x_{1} & 0.091 & 0.025 & 3.640 \\x_{2} & 0.93 & 0.290 & 3.207 \\x_{3} & 0.26 & 0.180 & 1.444 \\\hline\end{array}$

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \mathrm{F} \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}$
Interpret the coefficient $b _ { 2 }$ .

---

Definitions:

Democratic Behaviours

Actions that promote participation, equality, freedom of speech, and respect for all individuals in a group or society.

Participative Behaviours

The actions of individuals who are actively involved and contribute to group or organizational decision-making processes.

Leadership Approaches

Various strategies and styles employed by leaders to guide, influence, and ensure the fulfillment of goals by their followers.

Emotional Intelligence

The ability to recognize, understand, and manage one's own emotions and to recognize, understand, and influence the emotions of others.