An Economist Wanted to Develop a Multiple Regression Model to Enable

question 91

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & \mathrm { F } \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}\end{array}$$ What is the coefficient of determination? What does this statistic tell you?

---

Definitions:

Ph.D.

Stands for Doctor of Philosophy, a doctoral degree awarded by universities, representing the highest level of academic achievement in a particular field of study.

Harvard

An elite private university located in Cambridge, Massachusetts, known for its prestigious academic programs and historical significance.

Black Person

Refers to an individual of African descent or having a dark skin complexion.

Functionalists

Scholars who view society as a complex system whose parts work together to promote solidarity and stability.