## 34.8 Exercises

Selected answers are available in Sect. D.31.

Exercise 34.1 Draw a scatterplot with:

1. A negative correlation coefficient, with the value of $$r$$ very close to (but not equal to) $$-1$$.
2. A positive correlation coefficient, with the value of $$r$$ very close to (but not equal to) $$+1$$.
3. A correlation coefficient very close to $$0$$.

Exercise 34.2 A study (, p. 75) of American footballers measured the right-leg strengths $$x$$ of 13 players (using a weight lifting test), and the distance $$y$$ they punted a football (with their right leg) (Fig. 34.11).

1. The value of the correlation coefficient is 0.881. Compute the value of $$R^2$$, and explain what this means.
2. jamovi was used to study the correlation (Fig. 34.12). Using this output, perform a hypothesis test to determine if a correlation exists between punting distance and right-leg strength.
Exercise 34.3 A study examined the time taken to deliver soft drinks to vending machines using a sample of size $$n=25$$ (Fig. 34.13). To perform a test of the correlation coefficient, are the statistical validity conditions met?

Exercise 34.4 A study of hot mix asphalt created $$n=42$$ samples of asphalt and measured the volume of air voids and the bitumen content by weight (Fig. 34.14).

1. Using the plot, estimate the value of $$r$$.
2. The value of $$R^2$$ is 99.29%. What is the value of $$r$$? (Hint: Be careful!)
3. Would you expect the $$P$$-value testing $$H_0$$: $$\rho=0$$ to be small or large? Explain.
4. Would the test be statistically valid?

### References

Montgomery DC, Peck EA. Introduction to regression analysis. New York: Wiley; 1992.
Myers RH. Classical and modern regression with applications. second. Duxbury; 1990.
Panda RP, Das SS, Sahoo PK. Relation between bitumen content and percentage air voids in semi dense bituminous concrete. Journal of The Institution of Engineers (India): Series A. 2018;99(2):327–32.