Satisfaction with membership in a new religious movement.

How satisfied are people who have recently joined a new religious movement? To answer this question, German researchers collected data for a sample of 58 believers who had recently joined a new religious group (Applied Psychology:

An International Review, Apr. 2010). The dependent variable of interest was satisfaction level (y), measured quantitatively on an 11-point scale (where 0 = totally dissatisfied and 10 = totally satisfied). Two independent variables were used to predict satisfaction level: Needs (x1)—a measure of the level of needs one requires in a religion, and Supplies

(x2)—a measure of the level of supplies provided by the religion.

In theory, if the level of needs matches the level of supplies, one will be highly satisfied with the religion.

a. The researchers fitted a complete second-order model for E(y) as a function of x1 and x2. Write the equation of this model.

b. The regression results are reported in the table below.
Interpret the value of R2.

c. Use the R2 statistic to conduct a test of overall model adequacy. Test using a = .10.

d. Conduct a test to determine whether needs (x1) is curvilinearly related to satisfaction (y). Test using a = .10.

e. Conduct a test to determine whether supplies (x2) is curvilinearly related to satisfaction (y). Test using a = .10.
Independent Variable Estimated Beta Standard Error Needs (x1) .952 .780 Supplies (x2) 1.198 .766 Needs * Supplies 1x1x22 .356 .429 Needs * Needs 1x1 2 2 -.181 .302 Supplies * Supplies 1x2 2 2 -.755 .413 R2 = .402