115. When a scatter plot of bivariate data shows a pattern resembling an exponentially increasing or decreasing curve, the following multiplicative exponential model is often used: Y  aebx # e.

a. What does this multiplicative model imply about the relationship between  ln(Y) and x? Hint: Take logs on both sides of the model equation and let b0  ln(a), b1 

b,  ln(e), and suppose that e has a lognormal distribution.

b. The accompanying data resulted from an investigation of how ethylene content of lettuce seeds (y, in nL/g dry wt) varied with exposure time (x, in min) to an ethylene absorbent ( Ethylene Synthesis in Lettuce Seeds: Its Physiological Signi cance, Plant Physiol., 1972:

719—722).

x 2 20 20 30 40 50 60 70 80 90100 y 408 274 196 137 90 78 51 40 30 22 15 Fit the simple linear regression model to this data, and check model adequacy using the residuals.

e¿

Y¿

gˆ

1 T 

b

c. Is a scatter plot of the data consistent with the exponential regression model? Fit this model by rst carrying out a simple linear regression analysis using ln(y) as the dependent variable and x as the independent variable. How good a t is the simple linear regression model to the transformed data (the [x, ln(y)] pairs)? What are point estimates of the parameters a and b?

d. Obtain a 95% prediction interval for ethylene content when exposure time is 50 min. Hint:
First obtain a PI for ln(y) based on the simple linear regression carried out in (c).