Interpretation of coefficient of determination and scatter diagram.

The diagram below illustrates data with a

a. Negative correlation coefficient.
b. zero correlation coefficient
c. positive correlation coefficient
d. correlation coefficient equal to +1
e. none of these

2. A healthcare executive is using regression to predict total revenues. She is deciding whether or not to include both patient length of stay and insurance type in her model. Her first regression model only included patient length of stay. The resulting r² was .83, with an adjusted r² of 0.82 and her level of significance was 0.003. In the second model, she included both patient length of stay and insurance type. The r² was 0.84 and the adjusted r² was 0.80 for the second model and the level of significance did not change. Which of the following statements is true?

a. The second model is a better model.
b. The first is a better model.
c. The r² increased when additional variables were added because these variables significantly contribute to the prediction of total revenues.
d. The adjusted r² always increase when additional variables are added to the model.
e. None of these statements are true.

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