The authors of the article “Age, Spacing and Growth Rate of Tamarix as an Indication of Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia”

(Journal of Arid Environments [1982]: 43– 51) used a simple linear regression model to describe the relationship between y 5 vigor (average width in centimeters of the last two annual rings) and x 5 stem density (stems/

m2

). The estimated model was based on the following data. Also given are the standardized residuals.

x 4 5 6 9 14 y 0.75 1.20 0.55 0.60 0.65 St. resid. 20.28 1.92 20.90 20.28 0.54 x 15 15 19 21 22 y 0.55 0.00 0.35 0.45 0.40

(continued) St. resid. 0.24 22.05 20.12 0.60 0.52

a. What assumptions are required for the simple linear regression model to be appropriate?

b. Construct a normal probability plot of the standardized residuals. Does the assumption that the random deviation distribution is normal appear to be reasonable? Explain.

c. Construct a standardized residual plot. Are there any unusually large residuals?

d. Is there anything about the standardized residual plot that would cause you to question the use of the simple linear regression model to describe the relationship between x and y?