Презентация Correlation and Regression онлайн

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  • Тип файла:
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  • Всего слайдов:
    24 слайда
  • Для класса:
    1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:

№1 слайд
Chapter Correlation and
Содержание слайда: Chapter 9: Correlation and Regression 9.1 Correlation 9.2 Linear Regression 9.3 Measures of Regression and Prediction Interval
№2 слайд
Correlation Correlation A
Содержание 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
№3 слайд
Types of Correlation
Содержание слайда: Types of Correlation
№4 слайд
Example Constructing a
Содержание 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.
№5 слайд
Constructing a Scatter Plot
Содержание 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.
№6 слайд
Correlation Coefficient
Содержание 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
№7 слайд
Linear Correlation
Содержание слайда: Linear Correlation
№8 слайд
Calculating a Correlation
Содержание слайда: Calculating a Correlation Coefficient
№9 слайд
Example Finding the
Содержание слайда: Example: Finding the Correlation Coefficient Calculate the correlation coefficient for the advertising expenditures and company sales data. What can you conclude?
№10 слайд
Finding the Correlation
Содержание слайда: Finding the Correlation Coefficient Example Continued…
№11 слайд
Using a Table to Test a
Содержание 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.
№12 слайд
Hypothesis Testing for a
Содержание 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.
№13 слайд
Using the t-Test for
Содержание слайда: Using the t-Test for ρ
№14 слайд
Example t-Test for a
Содержание 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.
№15 слайд
Correlation and Causation The
Содержание 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?
№16 слайд
. Objectives Find the
Содержание слайда: 9.2 Objectives Find the equation of a regression line Predict y-values using a regression equation
№17 слайд
Residuals amp Equation of
Содержание 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.
№18 слайд
Finding Equation for Line of
Содержание слайда: Finding Equation for Line of Regression
№19 слайд
Solution Finding the Equation
Содержание 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.
№20 слайд
Example Predicting y-Values
Содержание 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
№21 слайд
. Measures of Regression and
Содержание 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
№22 слайд
Variation About a Regression
Содержание 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.
№23 слайд
The Standard Error of
Содержание 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.
№24 слайд
Prediction Intervals Two
Содержание 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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