11.12 Discrimination at work? A survey of 457 engineers in Canada was performed to identify the relationship of race, language proficiency, and location of training in finding work in the engineering field. In addition, each participant completed the Workplace Prejudice and Discrimination Inventory (WPDI), which is designed to measure perceptions of prejudice on the job, primarily due to race or ethnicity. The score of the WPDI ranged from 16 to 112, with higher scores indicating more perceived discrimination. The following table summarizes two multiple regression models used to predict an engineer’s WPDI score. The first explanatory variable indicates whether the engineer was foreign trained (x = 1) or locally trained (x = 0). The next set of seven variables indicate race and the last six are demographic variables.

	Model 1		Model 2
Explanatory variables	b	s(b)	b	s(b)
Foreign trained	0.55	0.21	0.58	0.22
Chinese			0.06	0.24
South Asian			−0.06	0.19
Black			−0.03	0.52
Other Asian			−0.38	0.34
Latin American			0.20	0.46
Arab			0.56	0.44
Other (not white)			0.05	0.38
Mechanical	−0.19	0.25	−0.16	0.25
Other (not electrical)	−0.14	0.20	−0.13	0.21
Masters/PhD	0.32	0.18	0.37	0.18
30–39 years old	−0.03	0.22	−0.06	0.22
40 or older	0.32	0.25	0.25	0.26
Female	−0.02	0.19	−0.05	0.19
R²	0.10		0.11

(a) The F statistics for these two models are 7.12 and 3.90, respectively. What are the degrees of freedom and P-value of each statistic?
(b) The F statistics for the multiple regressions are highly significant, but the R² are relatively low. Explain to a statistical novice how this can occur.
(c) Do foreign-trained engineers perceive more discrimination than do locally trained engineers? To address this, test if the first coefficient in each model is equal to zero versus the greater than alternative. Summarize your results.