Outliers · Exercise 10

The following table consists of one student athlete’s time (in minutes) to swim 2000 yards and the student’s heart rate (beats per minute) after swimming on a random sample of 10 days:

$$\begin{array}{cc}\text{Swim Time}& \text{Heart Rate}\\ \text{34.12}& \text{144}\\ \text{35.72}& \text{152}\\ \text{34.72}& \text{124}\\ \text{34.05}& \text{140}\\ \text{34.13}& \text{152}\\ \text{35.73}& \text{146}\\ \text{36.17}& \text{128}\\ \text{35.57}& \text{136}\\ \text{35.37}& \text{144}\\ \text{35.57}& \text{148}\end{array}$$

(a) Enter the data into your calculator and make a scatter plot.
(b) Use your calculator’s regression function to find the equation of the least-squares regression line. Add this to your scatter plot from part a.
(c) Explain in words what the slope and y-intercept of the regression line tell us.
(d) How well does the regression line fit the data? Explain your response.
(e) Which point has the largest residual? Explain what the residual means in context. Is this point an outlier? An influential point? Explain.

OpenStax, Introductory Statistics 2e · §12.6 Outliers · Exercise 10