A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 78

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 education are negatively linearly related?

Understand the development of agricultural policies and their effects on U.S. economy.

Identify the causes and consequences of the Great Depression and other economic downturns.

Understand the evolution of the U.S. as an industrial and economic power globally.

Understand the economic trends and job growth patterns since the millennium.

---

Definitions:

Marginal Revenue

The extra revenue obtained by selling an additional unit of a product or service.

International Marketing Agreement

An arrangement between parties from different countries to promote and distribute a product or service globally.

Cournot Duopolists

Firms in a duopoly (a market with only two producers) that set their output levels independently to maximize profits, anticipating the other's response.

Inverse Demand

A representation of demand that shows how the quantity demanded of a good or service varies inversely with price.