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

$$\mathrm { S } = 2.06 \quad \mathrm { R } - \mathrm { Sq } = 59.6 \%$$
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?

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Definitions:

Exchange Rate

The velocity at which one currency can be swapped for another, affecting global trade and investments.

Tax Impact

The effect that various forms of taxation have on individual or company finances, including income, capital gains, and sales taxes.

Floating Exchange Rate

A currency system where the value of a currency is allowed to fluctuate according to the foreign exchange market.

Fixed Exchange Rate

A currency system in which the value of a country's currency is tied to the value of another single currency, a basket of other currencies, or another measure of value, such as gold.