Statistics: The Art and Science of Learning from Data (4th Edition)

4th Edition

ISBN: 9780321997838

Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg

Publisher: PEARSON

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 13.3, Problem 29PB

Mental health again Refer to the previous exercise.

a. Report the test statistic and P-value for testing H₀: β₁ = β₂ = 0.
b. State the alternative hypothesis that is supported by the result in part a.
c. Does the result in part a imply that necessarily both life events and SES are needed in the model? Explain.

13.28 Regression for mental health A study in Alachua County, Florida, investigated an index of mental health impairment, which had y ¯ = 27.3 and s = 5.5. Two explanatory variables were x₁ = life events score (mean = 44.4, s = 22.6) and x₂ = SES (socioeconomic status, mean = 56.6, s = 25.3). Life events is a composite measure of the number and severity of major life events, such as death in the family, that the subject experienced within the past three years. SES is a composite index based on occupation, income, and education. The table shows data for 6 subjects. The complete data¹ for a random sample of 40 adults in the county is in the Mental Health data file on the book’s website. Some regression results are also shown.

a. Find the 95% confidence interval for β₁.
b. Explain why the interval in part a means that an increase of 100 units in life events corresponds to anywhere from a 4- to 17-unit increase in mean mental impairment, controlling for SES. (This lack of precision reflects the small sample size.)

y = mental impairment, x₁ = life events index, and x₂ = socioeconomic status

Chapter 13.3, Problem 29PB, Mental health again Refer to the previous exercise. a. Report the test statistic and P-value for , example 1

Chapter 13.3, Problem 29PB, Mental health again Refer to the previous exercise. a. Report the test statistic and P-value for , example 2

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 13.3, Problem 28PB

Chapter 13.3, Problem 30PB

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Chapter 13 Solutions

Statistics: The Art and Science of Learning from Data (4th Edition)

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Ch. 13.1 - Used cars The following data (also available from...Ch. 13.2 - Predicting sports attendance Keeneland Racetrack...Ch. 13.2 - Predicting weight Lets use multiple regression to...Ch. 13.2 - Prob. 14PB Ch. 13.2 - Price of used cars For the 19 used cars listed in...Ch. 13.2 - Prob. 16PB Ch. 13.2 - Softball data For the Softball data set on the...Ch. 13.2 - Slopes, correlations, and units In Example 2 on y...Ch. 13.2 - Predicting college GPA Using software with the...Ch. 13.3 - Predicting GPA For the 59 observations in the...Ch. 13.3 - Study time help GPA? Refer to the previous...Ch. 13.3 - Variability in college GPA Refer to the previous...Ch. 13.3 - Does leg press help predict body strength? Chapter...Ch. 13.3 - Prob. 24PB Ch. 13.3 - Interpret strength variability Refer to the...Ch. 13.3 - Any predictive power? Refer to the previous three...Ch. 13.3 - Predicting pizza revenue Aunt Ermas Pizza...Ch. 13.3 - Prob. 28PB Ch. 13.3 - Mental health again Refer to the previous...Ch. 13.3 - Prob. 30PB Ch. 13.3 - House prices Use software to do further analyses...Ch. 13.4 - Body weight residuals Examples 47 used multiple...Ch. 13.4 - Strength residuals In Chapter 12, we analyzed...Ch. 13.4 - Prob. 34PB Ch. 13.4 - Nonlinear effects of age Suppose you fit a...Ch. 13.4 - Prob. 36PB Ch. 13.4 - Why inspect residuals? When we use multiple...Ch. 13.4 - College athletes The College Athletes data set on...Ch. 13.4 - House prices Use software with the House Selling...Ch. 13.4 - Prob. 40PB Ch. 13.5 - U.S. and foreign used cars Refer to the used car...Ch. 13.5 - Prob. 42PB Ch. 13.5 - Predict using house size and condition For the...Ch. 13.5 - Quality and productivity The table shows data from...Ch. 13.5 - Predicting hamburger sales A chain restaurant that...Ch. 13.5 - Prob. 46PB Ch. 13.5 - House size and garage interact? Refer to the...Ch. 13.5 - Prob. 48PB Ch. 13.5 - Comparing sales You own a gift shop that has a...Ch. 13.6 - Prob. 50PB Ch. 13.6 - Prob. 51PB Ch. 13.6 - Prob. 52PB Ch. 13.6 - Prob. 53PB Ch. 13.6 - Prob. 54PB Ch. 13.6 - Prob. 55PB Ch. 13.6 - Prob. 56PB Ch. 13.6 - Prob. 57PB Ch. 13.6 - Prob. 58PB Ch. 13.6 - Prob. 59PB Ch. 13 - House prices This chapter has considered many...Ch. 13 - Prob. 61CP Ch. 13 - Prob. 62CP Ch. 13 - Prob. 63CP Ch. 13 - Prob. 64CP Ch. 13 - Prob. 65CP Ch. 13 - Prob. 66CP Ch. 13 - Prob. 67CP Ch. 13 - Prob. 68CP Ch. 13 - Prob. 69CP Ch. 13 - AIDS and AZT In a study (reported in the New York...Ch. 13 - Factors affecting first home purchase The table...Ch. 13 - Unemployment and GDP Refer to Exercise 13.67. When...Ch. 13 - Prob. 75CP Ch. 13 - Prob. 76CP Ch. 13 - Prob. 77CP Ch. 13 - Prob. 78CP Ch. 13 - Prob. 79CP Ch. 13 - True or false: Slopes For data on y = college GPA,...Ch. 13 - Prob. 81CP Ch. 13 - Lurking variable Give an example of three...Ch. 13 - Prob. 83CP Ch. 13 - Prob. 84CP Ch. 13 - Prob. 85CP Ch. 13 - Logistic versus linear For binary response...Ch. 13 - Prob. 87CP Ch. 13 - Prob. 88CP Ch. 13 - Prob. 89CP Ch. 13 - Prob. 90CP Ch. 13 - Prob. 91CP Ch. 13 - Prob. 92CP Ch. 13 - Prob. 93CP

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Solution Summary: The author explains that the test statistic and P-value are 9.49 and 0.000, which is less than any level of significance.

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Chapter 13 Solutions