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Week 4 Assignment Regression and Correlation Analysis: Exploring Relationships Between Variables

Application of regression and correlation in analyzing data relationships.

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Week 4AssignmentRegression and Correlation Analysis: Exploring Relationships Between Variables1.For each correlation coefficient below, calculate what proportion of variance is shared by the twocorrelated variables:We know that theproportion of variance is shared by the two correlated variables is the square of therespective correlation coefficient. Thus the required values are given below.a.r= 0.25Proportion of variance shared=0.252= 0.0625b.r= 0.33Proportion ofvariance shared=0.332= 0.1089c.r= 0.90Proportion of varianceshared=0.902= 0.81d.r= 0.14Proportion ofvariance shared=0.142= 0.01962.For each coefficient of determination below, calculate the value of the correlation coefficient:The respective correlation coefficient is the square root ofπ‘Ÿ2thus the answers are given below.a.r2= 0.54Correlation coefficient =√0.54= 0.7348b.r2= 0.13Correlation coefficient =√0.13= 0.3606c.r2= 0.29Correlation coefficient =√0.29= 0.5385d.r2= 0.07Correlation coefficient =√0.07= 0.26463.Suppose a researcher regressed surgical patients’ length of stay (dependent variable) in the hospital on ascale of functional ability measured 24 hours after surgery. Given the following, solve for the value ofthe intercept constant and write out the full regression equation:Mean length of stay = 6.5days; mean score on scale = 33; slope =-0.10Intercept = mean of dependent variable–slope* mean of independent variableοƒ°Intercept = 6.5–(-0.1)*33 = 9.8.The full regression model is,Y= 9.8 + 0.1*X

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Statistics

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