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Correlation and Regression Analysis

Correlation and Regression Analysis. By R. D. Wooten Statistical Consulting and Analytics Group (SCAG) University of South Florida. Correlation Analysis. Scatter plot of Turbidity (Y) over Forest (X). PCA Loading weights. Variances of principle components. Multiple Linear Regression.

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Correlation and Regression Analysis

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  1. Correlation and Regression Analysis By R. D. Wooten Statistical Consulting and Analytics Group (SCAG) University of South Florida

  2. Correlation Analysis

  3. Scatter plot of Turbidity (Y) over Forest (X)

  4. PCA Loading weights

  5. Variances of principle components

  6. Multiple Linear Regression Fitting six variables with eight data points is not recommended as it artificially inflates the coefficient of determination. The full model Y~X1+X2+ X3 + X4 + X5+X6 shows an ; however, nothing is significantly contributing as some of the variables are confounded. Moreover, I can make by including the interaction between X3 and X6; however, this is an exact solution with no measure of error - eight equations and eight unknowns. Consider the model Y~ X1 + X4 + X5 that is, Y ̂=11.2+0.35X1-0.24X4-4.42X5;R2=0.7311 This model explains 73.11% of the variance in Turbidity; that is, approximately 73% of the average turbidity is explained by the Developed, Wetland and Bare land with all variables found to be significant at the 5% level.

  7. PCA revisited

  8. Thank you Any questions?

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