A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 52

Essay

A statistician wanted to determine whether the demographic variables of age, education and income influence the number of hours of television watched per week. A random sample of 25 adults was selected to estimate the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
Where:
y = number of hours of television watched last week. $x _ { 1 }$ = age. $x _ { 2 }$ = number of years of education. $x _ { 3 }$ = income (in $1000s).
The computer output is shown below.
THE REGRESSION EQUATION IS
ŷ = $22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 22.3 & 10.7 & 2.084 \\x _ { 1 } & 0.41 & 0.19 & 2.158 \\x _ { 2 } & - 0.29 & 0.13 & - 2.231 \\x _ { 3 } & - 0.12 & 0.03 & - 4.00 \\\hline\end{array}$$ se = 4.51 R2 = 34.8%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 227 & 75.667 & 3.730 \\\text { Error } & 21 & 426 & 20.286 & \\\hline \text { Total } & 24 & 653 & & \\\hline\end{array}\end{array}$$ Test the overall validity of the model at the 5% significance level.

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Definitions:

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression, or a measure used to describe a statistical relationship.

Occurrence

An instance or event that takes place or happens, often used to refer to the frequency of events in a given context.

Predictive Validity

The extent to which a score or measure can predict future performance or behavior.

Test Outcome

The result or findings obtained from executing a statistical test or experiment.