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:

Insulin

A hormone produced in the pancreas that regulates the amount of glucose in the blood.

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A psychological and potentially life-threatening eating disorder characterized by an extreme fear of gaining weight and a distorted body image leading to self-starvation.

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A person's perceptions, thoughts, and feelings about their body.

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The consumption of large quantities of food in a short period of time, often accompanied by feelings of loss of control.