🗊Презентация Correlation and Regression

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Слайд 1


Chapter 9: Correlation and Regression 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Interval
Описание слайда:
Chapter 9: Correlation and Regression 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Interval

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

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Linear Correlation
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Linear Correlation

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Calculating a Correlation Coefficient
Описание слайда:
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?
Описание слайда:
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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Finding the Correlation Coefficient Example Continued…
Описание слайда:
Finding the Correlation Coefficient Example Continued…

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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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Hypothesis Testing for a Population Correlation Coefficient ρ A hypothesis test (one or two tailed) 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.
Описание слайда:
Hypothesis Testing for a Population Correlation Coefficient ρ A hypothesis test (one or two tailed) 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.

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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 For the advertising data, we previously calculated r ≈ 0.9129. Test the significance of this correlation coefficient. Use α = 0.05.
Описание слайда:
Example: t-Test for a Correlation Coefficient For the advertising data, we previously calculated r ≈ 0.9129. Test the significance of this correlation coefficient. Use α = 0.05.

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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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9.2 Objectives Find the equation of a regression line Predict y-values using a regression equation
Описание слайда:
9.2 Objectives Find the equation of a regression line Predict y-values using a regression equation

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Residuals & Equation of Line of Regression Residual The difference between the observed y-value and the predicted y-value for a given x-value on the line.
Описание слайда:
Residuals & Equation of Line of Regression Residual The difference between the observed y-value and the predicted y-value for a given x-value on the line.

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Finding Equation for Line of Regression
Описание слайда:
Finding Equation for Line of Regression

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Solution: Finding the Equation of a Regression Line To sketch the regression line, use any two x-values within the range of the data and calculate the corresponding y-values from the regression line.
Описание слайда:
Solution: Finding the Equation of a Regression Line To sketch the regression line, use any two x-values within the range of the data and calculate the corresponding y-values from the regression line.

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Example: Predicting y-Values Using Regression Equations The regression equation for the advertising expenses (in thousands of dollars) and company sales (in thousands of dollars) data is ŷ = 50.729x + 104.061. Use this equation to predict the expected company sales for the advertising expenses below: 1.5 thousand dollars : 1.8 thousand dollars 3. 2.5 thousand dollars
Описание слайда:
Example: Predicting y-Values Using Regression Equations The regression equation for the advertising expenses (in thousands of dollars) and company sales (in thousands of dollars) data is ŷ = 50.729x + 104.061. Use this equation to predict the expected company sales for the advertising expenses below: 1.5 thousand dollars : 1.8 thousand dollars 3. 2.5 thousand dollars

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9.3 Measures of Regression and Prediction Intervals (Objectives) Interpret the three types of variation about a regression line Find and interpret the coefficient of determination Find and interpret the standard error of the estimate for a regression line Construct and interpret a prediction interval for y
Описание слайда:
9.3 Measures of Regression and Prediction Intervals (Objectives) Interpret the three types of variation about a regression line Find and interpret the coefficient of determination Find and interpret the standard error of the estimate for a regression line Construct and interpret a prediction interval for y

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Variation About a Regression Line Total variation = The sum of the squares of the differences between the y-value of each ordered pair and the mean of y. Explained variation The sum of the squares of the differences between each predicted y-value and the mean of y.
Описание слайда:
Variation About a Regression Line Total variation = The sum of the squares of the differences between the y-value of each ordered pair and the mean of y. Explained variation The sum of the squares of the differences between each predicted y-value and the mean of y.

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The Standard Error of Estimate Standard error of estimate The standard deviation (se )of the observed yi -values about the predicted ŷ-value for a given xi -value. The closer the observed y-values are to the predicted y-values, the smaller the standard error of estimate will be.
Описание слайда:
The Standard Error of Estimate Standard error of estimate The standard deviation (se )of the observed yi -values about the predicted ŷ-value for a given xi -value. The closer the observed y-values are to the predicted y-values, the smaller the standard error of estimate will be.

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Prediction Intervals Two variables have a bivariate normal distribution if for any fixed value of x, the corresponding values of y are normally distributed and for any fixed values of y, the corresponding x-values are normally distributed.
Описание слайда:
Prediction Intervals Two variables have a bivariate normal distribution if for any fixed value of x, the corresponding values of y are normally distributed and for any fixed values of y, the corresponding x-values are normally distributed.

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