An Economist Wanted to Develop a Multiple Regression Model to Enable

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

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
ANALYSIS OF VARIANCE
$\begin{array}{|l|cccc|}\hline \text { Source of Variation } & \mathrm{df} & \mathrm{SS} & \mathrm{MS} & \mathrm{F} \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}$
What is the coefficient of determination? What does this statistic tell you?