A Student Used Multiple Regression Analysis to Study How Family $\begin{array}{lrr} & d f & S S \\\text { Regression }& 3 & 45.9634 \\\text { Residual } & 11 & 2.6218\\\text { Total }\end{array}$

question 53

Essay

A student used multiple regression analysis to study how family spending (y) is influenced by income (x₁), family size (x₂), and additions to savings (x₃).The variables y, x₁, and x₃ are measured in thousands of dollars.The following results were obtained. ANOVA
$\begin{array}{lrr} & d f & S S \\\text { Regression }& 3 & 45.9634 \\\text { Residual } & 11 & 2.6218\\\text { Total }\end{array}$
$\begin{array}{ll}&\text { Coefficients } & \text { Standard Error } \\\text { Intercept } &0.0136 & \\\mathrm{x}_{1}&0.7992 & 0.074 \\\mathrm{x}_{2}&0.2280 & 0.190 \\\mathrm{x}_{3}&-0.5796 & 0.920\end{array}$

a.
Write out the estimated regression equation for the relationship between the variables.
b.
Compute R². What can you say about the strength of this relationship?
c.
Carry out a test to determine whether y is significantly related to the independent variables. Use a .05 level of significance.
d.
Carry out a test to see if x₃ and y are significantly related. Use a .05 level of significance.

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Definitions:

Real GDP

Gross Domestic Product adjusted for inflation, representing the value of all goods and services produced over a specific time period in real terms.

Inflation Rates

The percentage rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling.

Unemployed Classification

A categorization for individuals who are without a job but are available to work and have actively sought employment within a specific timeframe.

Voluntary Reasons

Motives or causes that lead individuals to make choices freely without external coercion, often influencing personal and economic decisions.