Concept explainers
Although you might suspect that dissatisfied people would be the most likely individuals to participate in political activities in an attempt to change things, research tends to show just the opposite. Flavin and Keane (2011) found a positive relationship between life satisfaction and political participation, which included activities such as attending rallies, contributing to candidates, and displaying a yard sign. Following are data similar to those obtained in the study.
Life Satisfaction | Political Participation |
5 | 4 |
8 | 7 |
3 | 2 |
6 | 9 |
3 | 5 |
1 | 3 |
4 | 6 |
2 | 4 |
- a. Find the regression equation for predicting political participation from life satisfaction.
- b. Using α = .05, test the significance of the regression equation.
a.
Answer to Problem 24P
The regression equation of the data is
Explanation of Solution
Given info:
The given data are shown below,
Life satisfaction | Political participation |
5 | 4 |
8 | 7 |
3 | 2 |
6 | 9 |
3 | 5 |
1 | 3 |
4 | 6 |
2 | 4 |
Calculation:
Generally the linear regression equation is defined as
Formula to calculate
Formula to calculate the
Mean of the variable
Thus the mean of the variable
Mean of the variable
Thus the mean of the variable y is 5.
For calculating
Sr.no |
|
|
|
|
|
|
|
1 | 5 | 4 | 1 | -1 | 1 | 1 | -1 |
2 | 8 | 7 | 4 | 2 | 16 | 4 | 8 |
3 | 3 | 2 | -1 | -3 | 1 | 9 | 3 |
4 | 6 | 9 | 2 | 4 | 4 | 16 | 8 |
5 | 3 | 5 | -1 | 0 | 1 | 0 | 0 |
6 | 1 | 3 | -3 | -2 | 9 | 4 | 6 |
7 | 4 | 6 | 0 | 1 | 0 | 1 | 0 |
8 | 2 | 4 | -2 | -1 | 4 | 1 | 2 |
Total | 0 | 0 | 36 | 36 | 26 |
Where,
Substitute 0.723 for
Substitute 0.723 for
Thus, the regression equation is
b.
Answer to Problem 24P
The regression equation is significance at 5% level of significance.
Explanation of Solution
Calculation:
As per part (a) the regression equation is
Formula to calculate the Pearson correlation is,
Where variability of the variable x and y is
Mean of the variable
Thus the mean of the variable
Mean of the variable
Thus the mean of the variable y is 5.
For calculating
Sr.no |
|
|
|
|
|
|
|
1 | 5 | 4 | 1 | -1 | 1 | 1 | -1 |
2 | 8 | 7 | 4 | 2 | 16 | 4 | 8 |
3 | 3 | 2 | -1 | -3 | 1 | 9 | 3 |
4 | 6 | 9 | 2 | 4 | 4 | 16 | 8 |
5 | 3 | 5 | -1 | 0 | 1 | 0 | 0 |
6 | 1 | 3 | -3 | -2 | 9 | 4 | 6 |
7 | 4 | 6 | 0 | 1 | 0 | 1 | 0 |
8 | 2 | 4 | -2 | -1 | 4 | 1 | 2 |
Total | 0 | 0 | 36 | 36 | 26 |
Where,
Thus, the Pearson correlation is 0.722.
Set the null hypothesis
The alternative hypothesis
Formula to calculate the
Where,
Substitute 0.722 for
Substitute 0.722 for
Thus the
Thus the
Thus the
Substitute 18.766 for
Thus the
From the F-table, the value of
Decision rule:
If the calculated F-value is less than table F-value, then there is enough evidence to accept to reject the null hypothesis.
As
Thus, the regression equation is significance at 5% level of significance.
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Chapter 14 Solutions
Essentials of Statistics for the Behavioral Sciences
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt