The Practice of Statistics for AP - 4th Edition

4th Edition

ISBN: 9781429245593

Author: Starnes, Daren S., Yates, Daniel S., Moore, David S.

Publisher: Macmillan Higher Education

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Concept explainers

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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Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 3, Problem 7CRE

(a)

To determine

To find: The correlation increase, decrease or stay being the same.

(a)

Expert Solution

Answer to Problem 7CRE

The correlation decreases.

Explanation of Solution

Given information:

The correlation for all 50 states in the figure is 0.408.

The change in the correlation if on removing Hawaii is explained as below,

Correlation analysis is used to measure the strength of the association between variables. In other words, it can be said that correlation describes the linear associations between quantitative variables.

Since, correlation is sensitive to outliers, the correlation will be affected due to the data point Hawaii.

The data point of Hawaii is higher end outlier and it is above average corresponding to both the variables Maximum 24-hour participation and Maximum annual participation.

Since, the outlier is at the higher end, the correlation decreases by removing the higher end data point.

Therefore, the correlation decreases.

Conclusion:

The correlation decreases.

(b)

To determine

To analyse: The line that predicts the two least square lines.

(b)

Expert Solution

Answer to Problem 7CRE

The blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

Explanation of Solution

Given information:

Two least-squares lines ate shown on the graph. One was calculated using all 50 states, and the other omits Hawaii.

Identify the least squares line with the data point Hawaii and without the data point Hawaii:

It is known that the correlation decreases by removing the data point.

Since, there is a proportional relationship between the correlation coefficient and regression coefficient, the regression coefficient also decreases by removing the data point Hawaii.

The least squares line with small slope is the line without the data point Hawaii.

The least squares line with small slope is the line with the data point Hawaii.

Therefore, the blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

Conclusion:

The blue line is the least squares line with all 50 states and the red line is the least squares line without the data point Hawaii.

(c)

To determine

To analyse: The factor that will affect the correlation and the last-squares line

(c)

Expert Solution

Answer to Problem 7CRE

The switching the explanatory and response variables, the least squares line will change.

Explanation of Solution

Given information:

The Following would affect the correlation, s, and the last-squares line:

Measuring record precipitation in feet instead of inches for both variables
Switching the explanatory and response variables

The correlation will affect s and the least squares line:

Measuring record precipitation in feet instead of inches for both variables:

By changing the units the correlation will not change.
The standard error s will decrease by changing the units.
By changing the units, the slope of the least squares line will not change as the units of both the dependent and independent variables are changed but the intercept value will change.

Switching the explanatory and response variables:

By switching the explanatory and response variables, the correlation will not change.
The standard error s will decrease by switching the explanatory and response variables.
By switching the explanatory and response variables, the least squares line will change.

Conclusion:

The switching the explanatory and response variables, the least squares line will change.

Chapter 3, Problem 6CRE

Chapter 3, Problem 1PT

Chapter 3 Solutions

The Practice of Statistics for AP - 4th Edition

Ch. 3.1 - Prob. 1.1CYU Ch. 3.1 - Prob. 1.2CYU Ch. 3.1 - Prob. 2.1CYU Ch. 3.1 - Prob. 2.2CYU Ch. 3.1 - Prob. 2.3CYU Ch. 3.1 - Prob. 2.4CYU Ch. 3.1 - Prob. 2.5CYU Ch. 3.1 - Prob. 3.1CYU Ch. 3.1 - Prob. 3.2CYU Ch. 3.1 - Prob. 1E

Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.2 - Prob. 1.3CYU Ch. 3.2 - Prob. 1.4CYU Ch. 3.2 - Prob. 2.1CYU Ch. 3.2 - Prob. 3.1CYU Ch. 3.2 - Prob. 3.2CYU Ch. 3.2 - Prob. 3.3CYU Ch. 3.2 - Prob. 4.1CYU Ch. 3.2 - Prob. 4.2CYU Ch. 3.2 - Prob. 5.1CYU Ch. 3.2 - Prob. 5.2CYU Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - Prob. 47E Ch. 3.2 - Prob. 48E Ch. 3.2 - Prob. 49E Ch. 3.2 - Prob. 50E Ch. 3.2 - Prob. 51E Ch. 3.2 - Prob. 52E Ch. 3.2 - Prob. 53E Ch. 3.2 - Prob. 54E Ch. 3.2 - Prob. 55E Ch. 3.2 - Prob. 56E Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - Prob. 59E Ch. 3.2 - Prob. 60E Ch. 3.2 - Prob. 61E Ch. 3.2 - Prob. 62E Ch. 3.2 - Prob. 63E Ch. 3.2 - Prob. 64E Ch. 3.2 - Prob. 65E Ch. 3.2 - Prob. 66E Ch. 3.2 - Prob. 67E Ch. 3.2 - Prob. 68E Ch. 3.2 - Prob. 69E Ch. 3.2 - Prob. 70E Ch. 3.2 - Prob. 71E Ch. 3.2 - Prob. 72E Ch. 3.2 - Prob. 73E Ch. 3.2 - Prob. 74E Ch. 3.2 - Prob. 75E Ch. 3.2 - Prob. 76E Ch. 3.2 - Prob. 77E Ch. 3.2 - Prob. 78E Ch. 3.2 - Prob. 79E Ch. 3.2 - Prob. 80E Ch. 3.2 - Prob. 81E Ch. 3 - Prob. 1CRE Ch. 3 - Prob. 2CRE Ch. 3 - Prob. 3CRE Ch. 3 - Prob. 4CRE Ch. 3 - Prob. 5CRE Ch. 3 - Prob. 6CRE Ch. 3 - Prob. 7CRE Ch. 3 - Prob. 1PT Ch. 3 - Prob. 2PT Ch. 3 - Prob. 3PT Ch. 3 - Prob. 4PT Ch. 3 - Prob. 5PT Ch. 3 - Prob. 6PT Ch. 3 - Prob. 7PT Ch. 3 - Prob. 8PT Ch. 3 - Prob. 9PT Ch. 3 - Prob. 10PT Ch. 3 - Prob. 11PT Ch. 3 - Prob. 12PT Ch. 3 - Prob. 13PT

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