A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 76

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 $y =$ $$22.3 + 0.41 x _ { 1 } - 0.29 x _ { 2 } - 0.12 x _ { 3 }$$ $$\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 22.3 & 10.7 & 2.084 \\x _ { 1 } & 0.41 & 0.19 & 2.158 \\x _ { 2 } & - 0.29 & 0.13 & - 2.231 \\x _ { 3 } & - 0.12 & 0.03 & - 4.00 \\\hline\end{array}$$ S = 4.51 R-Sq = 34.8%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 227 & 75.667 & 3.730 \\\text { Error } & 21 & 426 & 20.286 & \\\hline \text { Total } & 24 & 653 & & \\\hline\end{array}\end{array}$$ Is there sufficient evidence at the 1% significance level to indicate that hours of television watched and age are linearly related?

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Definitions:

Statistically Significant

A mathematicallly determined indicator that the results of a study or experiment are unlikely to have occurred by chance.

Probability

The measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Observed Findings

Refers to results or outcomes that have been noticed and recorded from scientific experiments or observational studies.

Inferential Statistics

Statistical methods that allow researchers to make conclusions about populations based on samples.