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?

In Multiple Regression, When the Response Surface (The Graphical Depiction SεS _ { \varepsilon }Sε​

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In Multiple Regression, When the Response Surface (The Graphical Depiction $S _ { \varepsilon }$

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