Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
4th Edition
ISBN: 9780133860825
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Textbook Question
Chapter 3, Problem 61CP
Choose explanatory and response For the following pairs of variables, identify the response variable and the explanatory variable.
- a. Number of square feet in a house and assessed value of the house.
- b. Political party preference (Democrat, Independent, Republican) and gender.
- c. Annual income and number of years of education.
- d. Number of pounds lost on a diet and type of diet (low-fat, low-carbohydrate).
a.
Expert Solution
To determine
Find the response and the explanatory variables.
Explanation of Solution
Response variable:
A variable that is changed because of the influence of the explanatory variable is termed as response variable. The other name for response variable is dependent variable.
Explanatory variable:
A variable that can be changed or controlled in an experiment is termed as explanatory variable. The change in the response variable is explained by the explanatory variable.
The given pair of variables are number of square feet in a house and assessed value of the house. Here, the assessed value depends on the number of square feet of the house.
Therefore, the response variable is “assessed value” and the explanatory variable is “square feet”.
b.
Expert Solution
To determine
Discover the response and the explanatory variables.
Explanation of Solution
The given pair of variables are political party preference and gender. Here, the variable political party depends on the gender.
Therefore, the response variable is “political party” and the explanatory variable is “gender”.
c.
Expert Solution
To determine
Identify the response and the explanatory variables.
Explanation of Solution
The given pair of variables are annual income and number of years of education. Here, the variable annual income depends on the number of years of education.
Therefore, the response variable is “income” and the explanatory variable is “education”.
d.
Expert Solution
To determine
Obtain the response and the explanatory variables.
Explanation of Solution
The given pair of variables are number of pounds lost on diet and type of diet. Here, the variable pounds lost depends on the type of diet, which are categorized by low-fat and low-carbohydrate.
Therefore, the response variable is “pounds lost” and the explanatory variable is “type of diet”.
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Students have asked these similar questions
ons
12. A sociologist hypothesizes that the crime rate is higher in areas
with higher poverty rate and lower median income. She col-
lects data on the crime rate (crimes per 100,000 residents),
the poverty rate (in %), and the median income (in $1,000s)
from 41 New England cities. A portion of the regression results
is shown in the following table.
Standard
Coefficients
error
t stat
p-value
Intercept
-301.62
549.71
-0.55 0.5864
Poverty
53.16
14.22
3.74 0.0006
Income
4.95
8.26
0.60 0.5526
a.
b.
Are the signs as expected on the slope coefficients?
Predict the crime rate in an area with a poverty rate of
20% and a median income of $50,000.
3. Using data from 50 work
2. The owner of several used-car dealerships believes that the
selling price of a used car can best be predicted using the car's
age. He uses data on the recent selling price (in $) and age of
20 used sedans to estimate Price = Po + B₁Age + ε. A portion
of the regression results is shown in the accompanying table.
Standard
Coefficients
Intercept
21187.94
Error
733.42
t Stat p-value
28.89 1.56E-16
Age
-1208.25
128.95 -9.37
2.41E-08
a. What is the estimate for B₁? Interpret this value.
b. What is the sample regression equation?
C. Predict the selling price of a 5-year-old sedan.
ian income of $50,000.
erty rate of
13. Using data from 50 workers, a researcher estimates Wage =
Bo+B,Education + B₂Experience + B3Age+e, where Wage
is the hourly wage rate and Education, Experience, and Age
are the years of higher education, the years of experience, and
the age of the worker, respectively. A portion of the regression
results is shown in the following table. ni ogolloo bash
1
Standard
Coefficients error
t stat p-value
Intercept
7.87
4.09
1.93
0.0603
Education
1.44
0.34
4.24 0.0001
Experience
0.45
0.14
3.16
0.0028
Age
-0.01
0.08 -0.14 0.8920
a. Interpret the estimated coefficients for Education and
Experience.
b. Predict the hourly wage rate for a 30-year-old worker
with four years of higher education and three years of
experience.
Chapter 3 Solutions
Statistics: The Art and Science of Learning From Data, Books a la Carte Edition (4th Edition)
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