An investigation into the relationships between scatter plots, best fit lines, and correlation coefficients.

1. What are the largest and smallest values that r can be? What types of shapes make this happen?
2. How can you tell from the scatter plot whether r will positive or negative?
3. In what ways does r appear to be connected to the slope of the best fit line?
4. Create a plot where the r value is 0.7, and look at the best fit line for the plot. If you use this line to predict values of the points, how accurate will you be?
5. Create a plot where the r value is 0.2, and look at the best fit line for the plot. If you use this line to predict values of the points, how accurate will you be?
6. We can classify a relationship between variables as strong or weak. Which types of shapes would you consider strong correlations? Weak correlations?
7. Suppose you survey a class of students about the number of hours they spend on homework each night and the number of hours of sleep they get each night. You create a scatter plot with a correlation coefficient of r = - 0.74. What might that scatter plot look like? What could you conclude about the relationship between these two variables?