Final answer:
Heather's finding of a correlation coefficient of 1.0 between running time and calories burned means there is a perfect positive correlation, where an increase in running time leads to a proportional increase in calories burned.
Step-by-step explanation:
Heather has found a correlation coefficient (r) of 1.0 in her study of the relationship between running time on a treadmill and the number of calories burned. This result indicates a perfect positive correlation. This means that as the amount of time spent running increases, the number of calories burned increases proportionally, and every data point fits perfectly on a straight line with a positive slope. Therefore, when we have a correlation coefficient of 1.0, it signifies that we can predict with certainty that an increase in one variable (running time) will result in a proportional increase in the other variable (calories burned), assuming all conditions remain constant.
The concept of correlation is important to understand because it reveals the direction and strength of a relationship between two variables. However, we should not confuse correlation with causation; even with a perfect correlation, it does not mean one variable is causing the other to change only that they change together. In the context of Heather's study, the final option to the question is (c) There is a perfect positive correlation between running time and calorie burn.