🗊Презентация Correlation and regression

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Chapter 9 Correlation and Regression
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Chapter 9 Correlation and Regression

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Chapter Outline 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Intervals 9.4 Multiple Regression
Описание слайда:
Chapter Outline 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Intervals 9.4 Multiple Regression

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Section 9.1 Correlation
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Section 9.1 Correlation

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Section 9.1 Objectives Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation coefficient ρ using a table Perform a hypothesis test for a population correlation coefficient ρ Distinguish between correlation and causation
Описание слайда:
Section 9.1 Objectives Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation coefficient ρ using a table Perform a hypothesis test for a population correlation coefficient ρ Distinguish between correlation and causation

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Correlation Correlation A relationship between two variables. The data can be represented by ordered pairs (x, y) x is the independent (or explanatory) variable y is the dependent (or response) variable
Описание слайда:
Correlation Correlation A relationship between two variables. The data can be represented by ordered pairs (x, y) x is the independent (or explanatory) variable y is the dependent (or response) variable

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Correlation
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Correlation

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Types of Correlation
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Types of Correlation

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Example: Constructing a Scatter Plot A marketing manager conducted a study to determine whether there is a linear relationship between money spent on advertising and company sales. The data are shown in the table. Display the data in a scatter plot and determine whether there appears to be a positive or negative linear correlation or no linear correlation.
Описание слайда:
Example: Constructing a Scatter Plot A marketing manager conducted a study to determine whether there is a linear relationship between money spent on advertising and company sales. The data are shown in the table. Display the data in a scatter plot and determine whether there appears to be a positive or negative linear correlation or no linear correlation.

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Solution: Constructing a Scatter Plot
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Solution: Constructing a Scatter Plot

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Example: Constructing a Scatter Plot Using Technology Old Faithful, located in Yellowstone National Park, is the world’s most famous geyser. The duration (in minutes) of several of Old Faithful’s eruptions and the times (in minutes) until the next eruption are shown in the table. Using a TI-83/84, display the data in a scatter plot. Determine the type of correlation.
Описание слайда:
Example: Constructing a Scatter Plot Using Technology Old Faithful, located in Yellowstone National Park, is the world’s most famous geyser. The duration (in minutes) of several of Old Faithful’s eruptions and the times (in minutes) until the next eruption are shown in the table. Using a TI-83/84, display the data in a scatter plot. Determine the type of correlation.

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Solution: Constructing a Scatter Plot Using Technology Enter the x-values into list L1 and the y-values into list L2. Use Stat Plot to construct the scatter plot.
Описание слайда:
Solution: Constructing a Scatter Plot Using Technology Enter the x-values into list L1 and the y-values into list L2. Use Stat Plot to construct the scatter plot.

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Correlation Coefficient Correlation coefficient A measure of the strength and the direction of a linear relationship between two variables. The symbol r represents the sample correlation coefficient. A formula for r is The population correlation coefficient is represented by ρ (rho).
Описание слайда:
Correlation Coefficient Correlation coefficient A measure of the strength and the direction of a linear relationship between two variables. The symbol r represents the sample correlation coefficient. A formula for r is The population correlation coefficient is represented by ρ (rho).

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Correlation Coefficient The range of the correlation coefficient is -1 to 1.
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Correlation Coefficient The range of the correlation coefficient is -1 to 1.

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Linear Correlation
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Linear Correlation

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Calculating a Correlation Coefficient
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Calculating a Correlation Coefficient

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Calculating a Correlation Coefficient
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Calculating a Correlation Coefficient

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Example: Finding the Correlation Coefficient Calculate the correlation coefficient for the advertising expenditures and company sales data. What can you conclude?
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Example: Finding the Correlation Coefficient Calculate the correlation coefficient for the advertising expenditures and company sales data. What can you conclude?

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Solution: Finding the Correlation Coefficient
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Solution: Finding the Correlation Coefficient

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Solution: Finding the Correlation Coefficient
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Solution: Finding the Correlation Coefficient

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Example: Using Technology to Find a Correlation Coefficient Use a technology tool to calculate the correlation coefficient for the Old Faithful data. What can you conclude?
Описание слайда:
Example: Using Technology to Find a Correlation Coefficient Use a technology tool to calculate the correlation coefficient for the Old Faithful data. What can you conclude?

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Solution: Using Technology to Find a Correlation Coefficient
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Solution: Using Technology to Find a Correlation Coefficient

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Using a Table to Test a Population Correlation Coefficient ρ Once the sample correlation coefficient r has been calculated, we need to determine whether there is enough evidence to decide that the population correlation coefficient ρ is significant at a specified level of significance. Use Table 11 in Appendix B. If |r| is greater than the critical value, there is enough evidence to decide that the correlation coefficient ρ is significant.
Описание слайда:
Using a Table to Test a Population Correlation Coefficient ρ Once the sample correlation coefficient r has been calculated, we need to determine whether there is enough evidence to decide that the population correlation coefficient ρ is significant at a specified level of significance. Use Table 11 in Appendix B. If |r| is greater than the critical value, there is enough evidence to decide that the correlation coefficient ρ is significant.

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Using a Table to Test a Population Correlation Coefficient ρ Determine whether ρ is significant for five pairs of data (n = 5) at a level of significance of α = 0.01. If |r| > 0.959, the correlation is significant. Otherwise, there is not enough evidence to conclude that the correlation is significant.
Описание слайда:
Using a Table to Test a Population Correlation Coefficient ρ Determine whether ρ is significant for five pairs of data (n = 5) at a level of significance of α = 0.01. If |r| > 0.959, the correlation is significant. Otherwise, there is not enough evidence to conclude that the correlation is significant.

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Using a Table to Test a Population Correlation Coefficient ρ
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Using a Table to Test a Population Correlation Coefficient ρ

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Using a Table to Test a Population Correlation Coefficient ρ
Описание слайда:
Using a Table to Test a Population Correlation Coefficient ρ

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Example: Using a Table to Test a Population Correlation Coefficient ρ Using the Old Faithful data, you used 25 pairs of data to find r ≈ 0.979. Is the correlation coefficient significant? Use α = 0.05.
Описание слайда:
Example: Using a Table to Test a Population Correlation Coefficient ρ Using the Old Faithful data, you used 25 pairs of data to find r ≈ 0.979. Is the correlation coefficient significant? Use α = 0.05.

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Solution: Using a Table to Test a Population Correlation Coefficient ρ n = 25, α = 0.05 |r| ≈ 0.979 > 0.396 There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the duration of Old Faithful’s eruptions and the time between eruptions.
Описание слайда:
Solution: Using a Table to Test a Population Correlation Coefficient ρ n = 25, α = 0.05 |r| ≈ 0.979 > 0.396 There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the duration of Old Faithful’s eruptions and the time between eruptions.

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Hypothesis Testing for a Population Correlation Coefficient ρ A hypothesis test can also be used to determine whether the sample correlation coefficient r provides enough evidence to conclude that the population correlation coefficient ρ is significant at a specified level of significance. A hypothesis test can be one-tailed or two-tailed.
Описание слайда:
Hypothesis Testing for a Population Correlation Coefficient ρ A hypothesis test can also be used to determine whether the sample correlation coefficient r provides enough evidence to conclude that the population correlation coefficient ρ is significant at a specified level of significance. A hypothesis test can be one-tailed or two-tailed.

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Hypothesis Testing for a Population Correlation Coefficient ρ Left-tailed test Right-tailed test Two-tailed test
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Hypothesis Testing for a Population Correlation Coefficient ρ Left-tailed test Right-tailed test Two-tailed test

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The t-Test for the Correlation Coefficient Can be used to test whether the correlation between two variables is significant. The test statistic is r The standardized test statistic follows a t-distribution with d.f. = n – 2. In this text, only two-tailed hypothesis tests for ρ are considered.
Описание слайда:
The t-Test for the Correlation Coefficient Can be used to test whether the correlation between two variables is significant. The test statistic is r The standardized test statistic follows a t-distribution with d.f. = n – 2. In this text, only two-tailed hypothesis tests for ρ are considered.

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Using the t-Test for ρ
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Using the t-Test for ρ

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Using the t-Test for ρ
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Using the t-Test for ρ

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Example: t-Test for a Correlation Coefficient Previously you calculated r ≈ 0.9129. Test the significance of this correlation coefficient. Use α = 0.05.
Описание слайда:
Example: t-Test for a Correlation Coefficient Previously you calculated r ≈ 0.9129. Test the significance of this correlation coefficient. Use α = 0.05.

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Solution: t-Test for a Correlation Coefficient
Описание слайда:
Solution: t-Test for a Correlation Coefficient

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Correlation and Causation The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables. If there is a significant correlation between two variables, you should consider the following possibilities. Is there a direct cause-and-effect relationship between the variables? Does x cause y?
Описание слайда:
Correlation and Causation The fact that two variables are strongly correlated does not in itself imply a cause-and-effect relationship between the variables. If there is a significant correlation between two variables, you should consider the following possibilities. Is there a direct cause-and-effect relationship between the variables? Does x cause y?

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Correlation and Causation Is there a reverse cause-and-effect relationship between the variables? Does y cause x? Is it possible that the relationship between the variables can be caused by a third variable or by a combination of several other variables? Is it possible that the relationship between two variables may be a coincidence?
Описание слайда:
Correlation and Causation Is there a reverse cause-and-effect relationship between the variables? Does y cause x? Is it possible that the relationship between the variables can be caused by a third variable or by a combination of several other variables? Is it possible that the relationship between two variables may be a coincidence?

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Section 9.1 Summary Introduced linear correlation, independent and dependent variables and the types of correlation Found a correlation coefficient Tested a population correlation coefficient ρ using a table Performed a hypothesis test for a population correlation coefficient ρ Distinguished between correlation and causation
Описание слайда:
Section 9.1 Summary Introduced linear correlation, independent and dependent variables and the types of correlation Found a correlation coefficient Tested a population correlation coefficient ρ using a table Performed a hypothesis test for a population correlation coefficient ρ Distinguished between correlation and causation

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