Regresja liniowa wieloraka - prac.im.pwr.edu.plprac.im.pwr.edu.pl/~legut/listy/PS-12.pdf · Wykład...
Transcript of Regresja liniowa wieloraka - prac.im.pwr.edu.plprac.im.pwr.edu.pl/~legut/listy/PS-12.pdf · Wykład...
Wykład 12
Wydział Matematyki
Regresja liniowa wielorakaWspółczynnik determinacji, regresja krokowa
The Coefficient of Multiple Determination
The coefficient of multiple determination (R2, with 0 ≤ R2 ≤ 1) is the proportionof the variation in y that is explained by the multiple regression equation.
Example 1
The president of a large chain of fast-food restaurants has randomly selected10 franchises and recorded for each franchise the following information on lastyear’s net profit and sales activity.
For the 10 franchises, 77.19% of the variation in net profit is explained by the multiple regressionequation.
Testing the Significance of the Regression Equation
The multiple regression equation:
is based on sample data and is an estimate of the (unknown) population multiple regression equation:
If there really is no relationship between y and any of the x variables, all of the partial regression coefficients
in the population regression equation will be zero, and this is the basis on which we test the overall significance of our regression equation.
Testing the Significance of the Regression Equation
Example 1 Testing the Significance of the Regression Equation
The president of a large chain of fast-food restaurants has randomly selected10 franchises and recorded for each franchise the following information on lastyear’s net profit and sales activity.
Example 1 Testing the Significance of the Regression Equation
Using the F distribution tables to identify the critical value for F, the numberof degrees of freedom for the numerator will be k = 2; df for the denominator willbe (n - k - 1), or (10 - 2 - 1) = 7. Conducting the test at the 0.01 level of significance,the critical value is F = 9.55. The calculated test statistic (F = 11.85)exceeds the critical value, and H0 is rejected. At the 0.01 level, the multiple regressionequation is significant.
p value
Example 1 Testing the Significance of the Regression Equation
Solution in Statistica
Example 1
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Example 1
value for Fp value
coefficient of multiple determination
Example 2 - stepwise multiple linear regression
http://college.cengage.com/mathematics/brase/understandable_statistics/7e/students/datasets/mlr/frames/frame.html
Example 2 stepwise multiple linear regression
The data (Y, X1, X2, X3, X4) are by city.Y = death rate per 1000 residentsX1 = doctor availability per 100,000 residentsX2 = hospital availability per 100,000 residentsX3 = annual per capita income in thousands of dollarsX4 = population density people per square mileReference: Life In America's Small Cities, by G.S. Thomas
Example 2 stepwise multiple linear regression
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Example 2 stepwise multiple linear regression
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Example 2 stepwise multiple linear regression
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Example 2 stepwise multiple linear regression
Example 3 stepwise multiple linear regression
Job_prof.sta
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Example 3 stepwise multiple linear regression
The first four variables (Test1-Test4) represent four different aptitude tests that were administered to each of the 25 applicants for entry-level clerical positions in a company. Regardless of their test scores, all 25 applicants were hired. Once their probationary period had expired, each of these employees was evaluated and given a job proficiency rating (variable Job_prof). Using stepwise regression, the variables (or subset of variables) that best predict job proficiency will be analyzed. Thus, the dependent variable will be Job_prof and variables Test1-Test4 will be the independent or predictor variables.
Example 3 stepwise multiple linear regression
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Example 3 stepwise multiple linear regression
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Example 3 stepwise multiple linear regression
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Example 3 stepwise multiple linear regression
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Example 3 stepwise multiple linear regression
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Example 3 final solution
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