The paper ?Depression, Body Mass Index, and Chronic Obstructive Pulmonary Disease?A Holistic Approach? (International Journal of COPD [2016]:239?249) gave data on change in body mass index (BMI in kilograms/meter²) and change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The data in the table below are 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

a. Find the equation of the least-squares line that would allow you to predict change in depression score based on change in BMI.

b. Find the values of r² and s_e. Based on these values, do you think that the least-squares line does a good job of describing the relationship between change in depression score and change in BMI? Explain.

c. The following graph is a scatterplot of these data.

The least-squares line is also shown. Which observations are outliers? Do the observations with the largest residuals correspond to the patients with the largest change in BMI?

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Fitted Line Plot Depression score change = 6.873 + 5.078 BMI change 20 5.36559 R-Sq 23.5% 15 10 -0.5 0.0 0.5 1.0 1.5 BMI change (kg/m²) Depression score change