Question

Graphing Scatterplots and Trend Lines
Based on the trend lines you just generated, which of these statements are true? Check all that apply.
Both scatterplots had trend lines with positive slopes.
The same test score is expected from studying for 5 hours or sleeping for 5 hours.
There is no correlation between the test scores and the number of hours slept.
The regression line can predict the number of hours studied based on the number of hours slept.
There is evidence that those with higher test scores tended to sleep more the night before.

Answer 1

I don’t have the scatterplots or the trend‑line equations you generated, so I can’t check them directly. Here’s how you can decide which statements are true, and what to report back if you want me to pick for you.

What to look for in each scatterplot/trend line
- “Both scatterplots had trend lines with positive slopes.”
- True if the slope (m) of both regression lines is > 0. If one or both slopes ≤ 0, this statement is false.

- “The same test score is expected from studying for 5 hours or sleeping for 5 hours.”
- Compare the predicted test score from each regression at x = 5. If ŷ_study(5) = ŷ_sleep(5) (to within rounding), the statement is true; otherwise false.

- “There is no correlation between the test scores and the number of hours slept.”
- True if the slope of the sleep vs. score line is essentially zero and the correlation coefficient (r) is near 0 (and not statistically significant). If slope or |r| is meaningfully different from 0, there is a correlation (positive or negative).

- “The regression line can predict the number of hours studied based on the number of hours slept.”
- False in the usual sense unless you actually fit a model with hours studied as the response and hours slept as the predictor. A regression line fit to predict test score from hours slept does not directly predict hours studied from hours slept. You would need a separate regression with hours studied as y and hours slept as x.

- “There is evidence that those with higher test scores tended to sleep more the night before.”
- True if the sleep–score regression shows a positive slope and the relationship is reasonably strong/significant (positive r and not just random scatter). If the slope is negative or near zero, the statement is false.

If you want a definitive answer, tell me:
- the slopes (and intercepts) or the predicted scores at x=5 for each regression, and/or
- the correlation coefficients or R² values for each plot,
and I’ll mark which statements are true.