In the last few exercises we examined interactions between a quantitative predictor and a binary predictor, but we may also wish to use an interaction term for two quantitative variables. Consider the scatter plot of `happy`

versus `stress`

, this time colored by the quantitative variable `freetime`

, which represents the number of hours of free time a participant has on average each day.

If we divided the points into groups based on their `freetime`

value and fit a regression line for each group, would all the lines have the same slope?

- If we wanted to fit a line amongst the darker points (
`freetime`

between 5 and 6), the line might have a flat but negative slope. - In contrast, a line for lighter points (
`freetime`

between 0 and 2) might be steeper in slope.

Thus, if we wanted to fit a regression for this data, we might consider fitting several lines for different values of `freetime`

rather than a single one across all points. Much like in the previous exercises, we can achieve this by adding a term to the model for the interaction of `stress`

and `freetime`

.

### Instructions

**1.**

The scatter plot below shows data from the `plants`

dataset. The plot shows the amount of new growth in centimeters (`growth`

) versus the number of times a plant was watered monthly (`water`

), colored by amount of fertilizer the plant received (`fertilizer`

).

Imagine drawing in a regression line for each of three different groups: when the amount of fertilizer is 1 (very light points), 4 (medium), or 8 (dark). Just by inspecting the graph, estimate the slopes of these imaginary lines and save these in **script.py** as `slope1`

, `slope4`

, and `slope8`

, respectively. Do the slopes indicate that we may need to include an interaction term in our model?