The paper ?Depression, Body Mass Index, and Chronic Obstructive Pulmonary Disease?A Holistic Approach? (International Journal of COPD [2016]: 239?249) gives data on x = Change in body mass index (BMI in kg/m²)

y = Change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper.

BMI Change (kg/m²) .......................... Depression Score Change0.5 ......................................................................... 2120.5 ......................................................................... 90.0 ......................................................................... 40.1 ......................................................................... 40.7 ......................................................................... 60.8 ......................................................................... 71.0 ......................................................................... 131.5 ......................................................................... 141.1 ......................................................................... 171.0 ......................................................................... 180.3 ......................................................................... 120.3 ......................................................................... 14

The accompanying computer output is from Minitab.

a. What percentage of observed variation in depression score change at age 27 can be explained by the simple linear regression model??

b. Give an estimate of s and interpret this estimate.

c. Give an estimate of the average change in depression score change associated with a 1 kg/m^2?increase in BMI change.

d. Calculate a point estimate of the mean depression score change for a patient whose BMI change was 1.2 kg/m².

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Fitted Line Plot Depression score change = 6.873 + 5.078 BMI change 20. 5.36559 R-Sq R-Sq(adj) 15.8% 23.5% 15 10 -0.5 0.0 0.5 1.0 1.5 BMI change R-sq 5.36559 23.488 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.87 2.26 3.04 0.012 BMI change 5.08 2.90 1.75 0.110 1.00 Regression Equation Depression score change 6.87 + 5.08 BMI change %3! Depression score change