The scatterplot for age in years and length of legs is shown.

Question

Part A: Estimate and interpret the correlation coefficient.

Part B: Create an influential point for this graph that would cause the correlation to decrease. Explain your reasoning.

Answer 1

Step 1: Approximate your line of best fit

Step 2: Draw a line above and a line below the line of best fit that are both parallel to the line of best fit and also equidistant from it such that all the data is enclosed.

Step 3: Close off the ends of the data to make a large box around the data.

Step 4: Measure the length of that box and the width of that box and divided them (length/width) and call this number "k". This is pretty easy to do by just making a bunch of squares that are the same width as your box and lining them up:

Step 5: Calculate r as 1 - 1/k

k = 6.5 (there are 6.5 squares long over 1 square wide)

So r is approx 1 - 1/6.5 or approx 0.85

It's positive because it goes from lower left to upper right.

In reality, this isn't that great an estimate. The real r value is closer to 0.92

Whether r is 0.85 or 0.92, the interpretation is that there is a strong positive correlation between age and leg length.

Regarding an influential point, in order to get the correlation to decrease, we could add on outlier that would tend to "mess up" the linear relationship. Maybe a point like (8, 8) would do it or perhaps even (10, 8). That would drop the correlation to nearly 0.7