Which of the values is the best estimate of the correlation coefficient for the line of best fit for the data represented by the scatter plot?

Graph of a scatter plot, xy-plane, origin O. Horizontal axis scale 0 to 16, by 2’s. Vertical axis scale 0 to 60, by 5’s. Best fit line from approximately (6 comma 25) to near (14 comma 50). The data fits a linear model with a positive slope.

Technology required.

A study investigated the relationship between the amount of daily food waste measured in pounds and the number of people in a household. The data in the table displays the results of the study. 

Use graphing technology to create the line of best fit for the data in the table.

1. What is the equation of the line of best fit for this data? Round numbers to two decimal places.
2. What is the slope of the line of best fit? What does it mean in this situation? Is this realistic?
3. What is the \(y\)-intercept of the line of best fit? What does it mean in this situation? Is this realistic?

A table of values and the plot of the residuals for the line of best fit are shown. 

\(x\)	\(y\)
1	10
2	8
2.5	9.5
4	8
5	8
6	7.5
7.2	7
8.5	6

Graph of residuals, origin O. Horizontal axis scale 0 to 9, by 1’s. Vertical axis scale negative 1 point 5 to 1 point 5, by point 25’s. The points are discrete and have these points: (1 comma point 44), (2 comma negative 1 point 12), (2 point 5 comma point 6), (4 comma negative point 27), ( 5 comma point 2), (6 comma point 14), (7 point 2 comma point 168), (8 point 5 comma negative point 26).

1. Which point does the line estimate the best?
2. Which point does the line estimate the worst?

Tyler creates a scatter plot that displays the relationship between the grams of food a hamster eats, \(x\), and the total number of rotations that the hamster’s wheel makes, \(y\). Tyler creates a line of best fit and finds that the residual for the point \((1.4, 1250)\) is -132. The point \((1.2, 1364)\) has a residual of 117. Interpret the meaning of 117 in the context of the problem.