1.For each correlation coefficient below, calculate what proportion of variance is shared by the two correlated variables: r = 0.25 r = 0.33 r = 0.90 r = 0.14 2.For each coefficient of determination below, calculate the value of the correlation coefficient: r2 = 0.54 r2 = 0.13 r2 = 0.29 r2 = 0.07 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 4.Using the regression equation calculated in Exercise 3, compute the predicted value of Y (length of hospital stay) for patients with the following functional ability scores: X = 42 X = 68 X = 23 X = 10 5.Use the regression equation below for predicting graduate GPA for the three presented cases. Y′ = -1.636 + 0.793(undergrad GPA) + 0.004(GREverbal) – 0.0009(GREquant) +0.009(Motivation) Subject undergrad GPA GREverbal GREquant Motivation 1 2.9 560 540 55 2 3.2 550 590 65 3 3.4 600 550 70 6.Using the following information for R2, k, and N, calculate the value of the F statistic for testing the overall regression equation and determine whether F is statistically significant at the 0.05 level: R2 = 0.13, k = 5, N = 120 R2 = 0.53, k = 5, N = 30 R2 = 0.28, k = 4, N = 64 R2 = 0.14, k = 4, N = 64 7.According to the University of Chicago, as men age, their cholesterol level goes up. A new drug (XAB) is being tested to determine if it can lower cholesterol in aging males and at what dose. The data for the first test subject is below: Dose (mg) 2 3 5 6 8 10 Cholesterol level (mg/dL) 3101242011105220 Plot the data and include a regression line in StatCrunch. Copy and paste your graph into your Word document for full credit. What is the correlation coefficient r and what does it mean in this case? What is the coefficient of determination and what does it mean in this case? Is there a statistically significant correlation between dose and cholesterol level in this case? What is the predicted cholesterol level for a person taking a dose of 4 mg? What about if they are not taking the drug at all (0 mg)?