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

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Week 4 Assignment Regression and Correlation Analysis: Exploring Relationships Between Variables 1. For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables: We know that the proportion of variance is shared by the two correlated variables is the square of the respective correlation coefficient. Thus the required values are given below. a. r = 0. 25 Proportion of variance shared = 0.25 2 = 0.0625 b. r = 0.33 Proportion of variance shared = 0.33 2 = 0.1089 c. r = 0.9 0 Proportion of variance shared = 0.90 2 = 0.81 d. r = 0.14 Proportion of variance shared = 0.14 2 = 0.0196 2. For each coefficient of determination below, calculate the value of the correlation coefficient: The respective correlation coefficient is the square root of 𝑟 2 thus the answers are given below. a. r 2 = 0.54 Correlation coefficient = √ 0 . 54 = 0.7348 b. r 2 = 0.13 Correlation coefficient = √ 0 . 13 = 0.3606 c. r 2 = 0.29 Correlation coefficient = √ 0 . 29 = 0.5385 d. r 2 = 0.07 Correlation coefficient = √ 0 . 07 = 0.2646 3. Suppose a researcher regressed surgical patients’ length of stay (dependent variable) in the hospital on a scale of functional ability measured 24 hours after surgery. Given the following, solve for the value of the intercept constant and write out the full regression equation: Mean length of stay = 6.5days; mean score on scale = 33; slope = - 0.10 Intercept = mean of dependent variable – slope* mean of independent variable  Intercept = 6.5 – ( - 0.1)*33 = 9.8. The full regression model is, Y = 9.8 + 0.1* X
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