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BY R. D. WOOTEN STATISTICAL CONSULTING AND ANALYTICS GROUP (SCAG) UNIVERSITY OF SOUTH FLORIDA Correlation and Regression Analysis

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Correlation Analysis DevelopedAgricultureForestWetlandBare landRangeland Developed1 Agriculture0.18101 Forest-0.0686-0.18031 Wetland0.52550.1402-0.87541 Bare land0.4918-0.16260.7282-0.40061 Rangeland-0.1124-0.32790.9853-0.86340.68861 Turbidity: All stations (turb <24)0.08170.46660.0755-0.0380-0.21210.0233

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

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PCA Loading weights PC1PC2PC3PC4PC5PC6PC7 DevelopedX10.370.08-0.86-0.13-0.27-0.110.08 AgricultureX20.33-0.930.02-0.010.140.030 ForestX3-0.11-0.04-0.140.040.07-0.2-0.96 WetlandX40.770.350.160.210.450.11-0.11 Bare landX5-0.010-0.07-0.17-0.150.95-0.2 RangelandX6-0.39-0.04-0.450.30.710.160.14 Turbidity: All stations (turb <24)Y0.01-0.07-0.020.9-0.410.09-0.01

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Variances of principle components

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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;R 2 =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.

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PCA revisited PC1PC2PC3PC4 DevelopedX10.503-0.861 WetlandX40.8650.5 Bare landX5-0.1650.982 Turbidity: All stations (turb <24)Y0.9860.163

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ANY QUESTIONS? Thank you

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