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Research Methods I

Review. Multiple regression analyses includes two or more independent variables in the prediction of the dependent variableTwo kinds of multiple regression analyses:Orthogonal (IVs are not related)Non-orthogonal (IVs are related)Regression plane (best-fit plane like best-fit line)Y' = a bX

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Research Methods I

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    1. Research Methods I Back to Multiple Regression

    2. Review Multiple regression analyses includes two or more independent variables in the prediction of the dependent variable Two kinds of multiple regression analyses: Orthogonal (IVs are not related) Non-orthogonal (IVs are related) Regression plane (best-fit plane like best-fit line) Y = a + bX + cT

    3. Calculating the Regression Plane

    4. Evaluate the Quality of the Prediction Calculate the Multiple Correlation Coefficient Expresses the strength of the relationship between several independent variables and one dependent variable R2Y.XT (R squared of Y explained by X and T) Calculate F ratio Evaluate probability of obtaining the relationship by chance

    5. Calculate F-ratio Based on F-ratio formula for regression with one independent variable Takes number of independent variables into account K = number of independent variables used to predict the dependent variable ?1 = K ?2 = S K 1 If F-ratio is larger then F-critical then reject the null hypothesis and accept alternative hypothesis (linear relationship between the two independent variables and the dependent variable)

    6. Importance of Each Variable in Prediction Importance of variable X Correlation coefficient between and X Proportion of prediction of Y accounted for by X Importance of variable T Correlation coefficient between and T Proportion of prediction of Y accounted for by T r2.X + r2.T = 1

    7. Importance of Each Variable for Dependent Variable Importance of variable X Correlation coefficient between Y and X Proportion of prediction of Y accounted for by X Importance of variable T Correlation coefficient between Y and T Proportion of prediction of Y accounted for by T r2Y.X + r2Y.T = R2Y.XT

    8. Significance of Each IV F-test for simple coefficients of correlation For each independent variable Tests if there is a linear relationship between one independent variable and dependent variable ?1 = 1 ?2 = S K - 1

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