An Economist Wanted to Develop a Multiple Regression Model to Enable

question 104

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

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Definitions:

Developmental Psychology

The branch of psychology that studies how people grow and change throughout their lifespan, from infancy to old age, including cognitive, emotional, and social development.

Immediate Family

Closest family members, typically including parents, siblings, and children, considered as direct relatives.

Adult Years

The period in a person's life following adolescence, characterized by the assumption of adult roles and responsibilities.

Stage Theory

The concept that development and progress in certain fields occur through distinct phases or stages, each with its own challenges and characteristics.