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, presented in Exercise 9.54 (p. 512). Recall that each in a sample of n = 55 native Spanish-speaking adults 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 coefficient of determination, r2, for each model is listed in the accompanying table. Give a practical interpretation of each of these values.
Independent Variable (x) | r2 |
SG score | .002 |
SR score | .099 |
ER score | .078 |
Exercise 9.54
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 regression was used to model the ESLR score (y) as a function of each of the other exam scores (x). The results are summarized in the following table:
Independent variable (x) | p-value for testing H0: β1 = 0 |
SG score | .739 |
SR score | .012 |
ER score | .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?
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