Fundamentals of Statistics (5th Edition)

5th Edition

ISBN: 9780134510026

Author: Sullivan

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 12.3, Problem 21AYU

Age versus HDL Cholesterol A doctor wanted to determine whether there is a relation between a male’s age and ins HDL (so-called good) cholesterol. He randomly selected 17 of his patients and determined their HDL levels. He obtained the data shown in the next column.

Age, x	HDL Cholesterol, y
38	57
42	54
46	34
32	56
55	35
52	40
61	42
61	38
26	47
38	44
66	62
30	53
51	36
27	45
52	38
49	55
39	28

Source: Data based on information obtained from the National Center for Health Statistics

a. Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appeals to exist between age and HDL cholesterol?
b. Determine the least-squares regression equation from the sample data.
c. Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the α = 0.01 level of significance.
d. Assuming the residuals are normally distributed, construct a 95% confidence interval for the slope of the true least-squares regression line.
e. For a 42-year-old male patient who visits the doctor’s office, would you recommend using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient? Why? What would be a good estimate for the HDL cholesterol of this patient?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 12.3, Problem 20AYU

Chapter 12.3, Problem 22AYU

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Chapter 12 Solutions

Fundamentals of Statistics (5th Edition)

Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYU Ch. 12.1 - Prob. 8AYU Ch. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...

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Solution Summary: The author explains that there is no linear relation between age and HDL cholesterol, and the least-square regression equation from the sample data.

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