Question 6.71
36. Scientists are concerned that rising sea temperatures will have an adverse effect on coral growth. A small study on this issue produced the data in the table below:
| Temperature (°C), | 29.7 | 29.9 | 30.2 | 30.2 | 30.5 | 30.7 | 30.9 |
| Coral growth (mm), | 2.63 | 2.58 | 2.60 | 2.48 | 2.26 | 2.38 | 2.26 |
- Make a scatterplot of coral reef growth versus the average sea surface temperature. Do these data tend to support or refute the scientists’ concern? Explain.
- After drawing a scatterplot, Jason thought that the line through the points (29.7, 2.63) and (30.9, 2.26) did a good job summarizing the pattern of these data. Draw Jason’s line on your scatterplot from part (a). Do you agree with Jason?
Verify that Jason’s line can be represented by the following equation:
Show the calculations for obtaining the slope and y-intercept.
Carol used her calculator to find the equation of something called the median-median line. The equation of her line is
Using the least-squares criterion (i.e., the line with the smaller sum of squares of residual errors), which line is better, Jason’s or Carol’s? Justify your answer. (Feel free to use spreadsheet software or operations on calculator lists to respond to this question.)