A Statistician Wanted to Determine Whether the Demographic Variables of Age

question 61

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

---

Definitions:

First Born

The term refers to the first child born to a set of parents, often studied in developmental psychology for its potential impact on personality and behaviors.

Primary Sexual Characteristics

The physical structures directly involved in reproduction, present at birth.

Complex Changes

In the context of psychology, this could refer to the multifaceted adjustments in behavior or cognition that occur as a result of various internal and external factors. If not applicable, NO.

Menarche

The onset of menstruation, marking the beginning of a female's reproductive years.