English as a second language reading ability. Refer to the Bilingual Research Journal (Summer 2006) study of the relationship of Spanish (first language) grammatical knowledge to English (second language) reading, Exercise. Recall that three simple linear regressions were used to model the English reading (ESLR) score (y) as a function of Spanish grammar (SG), Spanish reading (SR), and English grammar (EG), respectively.
(a) If the researchers want to predict the ESLR score (y) of a native Spanish-speaking adult who scored x = 50% in Spanish grammar (x), how should they proceed?
(b) If the researchers want to estimate the mean ESLR score, E(y), of all native Spanish speaking adults who scored x = 70% in Spanish grammar (x), how should they proceed?
Exercise
English as a second language reading ability. What are the factors that allow a native Spanish speaking person to understand and read English? A study published in the Bilingual Research Journal (Summer 2006) investigated the relationship of Spanish (first language) grammatical knowledge to English (second language) reading. The study involved a sample of n = 55 native Spanish-speaking adults who were students in an English as a second language (ESL) college class. Each student took four standardized exams: Spanish grammar (SG), Spanish reading (SR), English grammar (EG), and English reading (ESLR). Simple linear regressions were used to model the ESLR score (y) as a function of each of the other exam scores (x). The results are summarized in the table.
|
Independent variable (x)
|
p-value for testing H0: β1 = 0
|
|
SG score
|
.739
|
|
SR score
|
.012
|
|
ER scor e
|
.022
|
(a) At α = .05, is there sufficient evidence to indicate that ESLR score is linearly related to SG score?
(b) At α = .05, is there sufficient evidence to indicate that ESLR score is linearly related to SR score?
(c) At α = .05, is there sufficient evidence to indicate that ESLR score is linearly related to ER score?