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Suppose you work at the Wisconsin Department of Natural Resources (DNR) and you have been assigned to understand the relationship between the amount of toxic blue-green algae growing in a lake (i.e. Y) and the lake's water temperature (i.e. X); from DNR about blue-green algae growth in Wisconsin lakes. You ran a simple linear regression to obtain an estimate of the slope and intercept of the best fit line and find that there is a statistically significant relationship between temperature and blue-green algae growth.
Suppose for a new project, you wish to instead use the amount of blue-green algae growth to predict the lake's temperature; in other words, the manager wants you to define X to be the amount of blue-green algae growth and Y to be lake's temperature (i.e. you exchanged the definitions of X and Y).
For each of the following, explain if it will increase, decrease, stay the same, or change in some other way (or if it's impossible to say without more information).
1. Slope of the new line
2. Intercept of the new line
3. T-statistic of the slope of the new line
4. R² of the new line
(*Hint: you may find it helpful to use a few examples to "test" different situations.*)
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