The article “Readability of Liquid Crystal Displays: A Response Surface” (Human Factors, 1983: 185–190) used a multiple regression model with four independent variables to study accuracy in reading liquid crystal displays. The variables were y
error percentage for subjects reading a four-digit liquid crystal display x1
level of backlight (ranging from 0 to 122 cd/m2

)

x2
character subtense (ranging from .025° to 1.34°)

x3
viewing angle (ranging from 0° to 60°)

x4
level of ambient light (ranging from 20 to 1500 lux)

The model fit to data was Y
0 1x1 2x2 3 x3

4 x4 !. The resulting estimated coefficients were

ˆ

0
1.52, ˆ

1
.02, ˆ

2
1.40, ˆ

3
.02, and ˆ

4
.0006.

a. Calculate an estimate of expected error percentage when x1
10, x2
.5, x3
50, and x4
100.

b. Estimate the mean error percentage associated with a backlight level of 20, character subtense of .5, viewing angle of 10, and ambient light level of 30.

c. What is the estimated expected change in error percentage when the level of ambient light is increased by 1 unit while all other variables are fixed at the values given in part (a)?

Answer for a 100-unit increase in ambient light level.

d. Explain why the answers in part

(c) do not depend on the fixed values of x1, x2, and x3. Under what conditions would there be such a dependence?

e. The estimated model was based on n
30 observations, with SST
39.2 and SSE
20.0. Calculate and interpret the coefficient of multiple determination, and then carry out the model utility test using 
.05.