5th Edition

ISBN: 9781285463186

Author: Jessica M. Utts, Robert F. Heckard

Publisher: Brooks Cole

Concept explainers

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 3, Problem 3.18E

The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is
y ^ = 113.6 − 1.01 x

What is the slope of the line? Interpret the slope in terms of how the mean August temperature is affected by a change in latitude.
Estimate the mean August temperature for a city with latitude of 32.

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 3, Problem 3.17E

Chapter 3, Problem 3.19E

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Chapter 3 Solutions

Mind on Statistics

Ch. 3 - For each of the following pairs of variables, is...Ch. 3 - For each of the following pairs of variables, is...Ch. 3 - The figure for this exercise is a scatter plot of...Ch. 3 - Prob. 3.4E Ch. 3 - Prob. 3.5E Ch. 3 - Prob. 3.6E Ch. 3 - Prob. 3.7E Ch. 3 - Prob. 3.8E Ch. 3 - The data in the following table are the geographic...Ch. 3 - Refer to the latitude and temperature data in the...

Ch. 3 - Prob. 3.11E Ch. 3 - The following table shows sex, height (inches),...Ch. 3 - Prob. 3.13E Ch. 3 - Refer to Exercise 3.13 in which a regression...Ch. 3 - Prob. 3.15E Ch. 3 - Prob. 3.16E Ch. 3 - The equation for converting a temperature from x =...Ch. 3 - The average August temperatures (y) and geographic...Ch. 3 - A regression equation for y = handspan (cm) and x...Ch. 3 - Imagine a regression line that relates y average...Ch. 3 - Prob. 3.21E Ch. 3 - The figure for Exercise 3.8 is a scatterplot of...Ch. 3 - Refer to Exercise 3.22. Predict the pulse rate...Ch. 3 - The average January temperatures (y) and...Ch. 3 - Prob. 3.25E Ch. 3 - Prob. 3.26E Ch. 3 - Prob. 3.27E Ch. 3 - Remember that r2 can be expressed as a proportion...Ch. 3 - Prob. 3.29E Ch. 3 - Prob. 3.30E Ch. 3 - Prob. 3.31E Ch. 3 - Prob. 3.32E Ch. 3 - Prob. 3.33E Ch. 3 - Explain how two variables can have a perfect...Ch. 3 - Prob. 3.35E Ch. 3 - Prob. 3.36E Ch. 3 - The figure for this exercise (below) shows four...Ch. 3 - Refer to the figure for the previous exercises. In...Ch. 3 - Prob. 3.39E Ch. 3 - Prob. 3.40E Ch. 3 - Prob. 3.41E Ch. 3 - Prob. 3.42E Ch. 3 - Prob. 3.43E Ch. 3 - The correlation between latitude and average...Ch. 3 - Prob. 3.45E Ch. 3 - Prob. 3.46E Ch. 3 - In a regression analysis, the total sum of squares...Ch. 3 - Prob. 3.48E Ch. 3 - Suppose you know that the slope of a regression...Ch. 3 - Prob. 3.50E Ch. 3 - Prob. 3.51E Ch. 3 - Prob. 3.53E Ch. 3 - Prob. 3.54E Ch. 3 - Refer back to Exercise 3.7 about stopping distance...Ch. 3 - Prob. 3.56E Ch. 3 - Prob. 3.57E Ch. 3 - Prob. 3.58E Ch. 3 - Prob. 3.59E Ch. 3 - Prob. 3.60E Ch. 3 - Prob. 3.61E Ch. 3 - Prob. 3.62E Ch. 3 - Prob. 3.63E Ch. 3 - Prob. 3.64E Ch. 3 - Prob. 3.65E Ch. 3 - Prob. 3.66E Ch. 3 - Prob. 3.67E Ch. 3 - Prob. 3.68E Ch. 3 - Prob. 3.69E Ch. 3 - Prob. 3.70E Ch. 3 - Prob. 3.71E Ch. 3 - Given tickets for traffic violations than drivers...Ch. 3 - Prob. 3.73E Ch. 3 - Prob. 3.74E Ch. 3 - Prob. 3.75E Ch. 3 - Prob. 3.76E Ch. 3 - Prob. 3.77E Ch. 3 - Prob. 3.78E Ch. 3 - Prob. 3.79E Ch. 3 - The heights (inches) and foot lengths (cm) of 33...Ch. 3 - Prob. 3.81E Ch. 3 - The winning time in the Olympic men’s 500-meter...Ch. 3 - Prob. 3.83E Ch. 3 - Prob. 3.84E Ch. 3 - Prob. 3.86E Ch. 3 - Prob. 3.87E Ch. 3 - Prob. 3.88E Ch. 3 - Prob. 3.89E Ch. 3 - Use the dataset ceodata0t on the companion website...Ch. 3 - Prob. 3.91E Ch. 3 - Prob. 3.92E Ch. 3 - Prob. 3.93E Ch. 3 - Prob. 3.94E Ch. 3 - Prob. 3.95E Ch. 3 - Prob. 3.96E Ch. 3 - Prob. 3.97E Ch. 3 - Prob. 3.98E Ch. 3 - Prob. 3.99E Ch. 3 - Prob. 3.100E

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Solution Summary: The author explains that the slope of the given regression equation is -1.01. As the latitude value increases by 1 then the august temperature decreases by 1.01 simultaneously.

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