A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 21

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 227 & 75.667 & 3.730 \\\text { Error } & 21 & 426 & 20.286 & \\\hline \text { Total } & 24 & 653 & & \\\hline\end{array}\end{array}$$ What is the coefficient of determination? What does this statistic tell you?

---

Definitions:

Natural Justice

Procedural fairness in decision-making.

Business Operations

The ongoing, routine activities involved in the running of a business for the purpose of producing value for the stakeholders.

Administrative Laws

A branch of public law that regulates the activities of administrative agencies of government, including rulemaking, adjudication, or the enforcement of specific regulatory agendas.

Criminal Laws

Laws that prohibit certain behaviors and actions considered harmful to society, and outline punishments for breaches of these laws.