A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 34

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%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 227 & 75.667 & 3.730 \\\text { Error } & 21 & 426 & 20.286 & \\\hline \text { Total } & 24 & 653 & & \\\hline\end{array}\end{array}$$ Test the overall validity of the model at the 5% significance level.

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Definitions:

Reinforcement

In behavioral psychology, a process by which a behavior is strengthened or increased by its consequences.

Positive Reinforcement

A method of behavior modification that involves rewarding a desired behavior in order to increase the likelihood of it occurring again.

Watson

Psychologist John B. Watson, known as the father of behaviorism, emphasized the study of observable behavior.

Thorndike

An American psychologist known for his work on learning theory that led to the development of operant conditioning within behaviorism.