An Economist Wanted to Develop a Multiple Regression Model to Enable

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
$\begin{array}{|l|cccc|}\hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 288 & 96 & 22.647 \\\text { Error } & 46 & 195 & 4.239 & \\\hline \text { Total } & 49 & 483 & & \\\hline\end{array}$
Test at the 10% significance level to determine whether annual household income and annual family clothes expenditure are linearly related.