Reference no: EM13244655

I) Analyzing and interpreting data

Dr. Fuller wanted to study whether Latino children's English ability affects their learning outcomes inkindergarten.

For this study Dr. Fuller analyzed data from the Early Childhood Longitudinal Study (ECLS-K) Kindergarten Class of 1998-99, sponsored by the National Center of Education Statistics..Using a multistage probabilistic sampling design, the ECLS-K is based on a nationally representative sample of approximately 20,000 kindergarteners. Dr. Fuller analyzed a randomly selected subsample of Latino children.

The variables analyzed are the following:

1) Math test score in kindergarten:  Range from 6 to 84 points. Math tests are curriculum-based assessments based on the National Assessment of Educational Progress framework of content areas and domains. 

2)  English ability (OLDS), whichwas measured by students' test scores on the English Oral Language Development Scale taken in the fall of kindergarten.  The ECLS-K study used the OLDS to determine whether students from non-English speaking homes had the necessary minimum English skills to take cognitive assessments in English. The OLDS scores range from 0-60 points.

Given that socioeconomic status is such a strong predictor of learning outcomes, he decided to include this variable in his analyses.

3) Students' socioeconomic status (SES) isa standardized measure with a mean of 0 and astandard deviation of 1.  It represents student families'socioeconomic status based on mothers' and fathers' education, mothers' and fathers'occupational status, and householdincome, measured in the fall of kindergarten and in thespring of first grade. 

Dr Fuller gave you the following tables/analyses and went traveling with his son to Turkey. You are responsible for finishing the required computations and reporting the mainresults of his study. He ran several analyses, including descriptive statistics, bivariate correlations, and several regression models (shown in the next page).

Table 1:Descriptive Information

Variable	Obs	Mean	Std. Dev	Min	Max
Math score	2108	17.57009	7.313663	6.24	71
SES	2108	-.4145897	.7070371	-3.515	2.785
OLDS	2108	36.42884	18.71745	0	60

Table 2: Bivariate correlation(obs=2108)

	Math score	SES	OLDS
Math score	1.0000
SES	0.4711	1.0000
OLDS	0.3639	0.4807	1.0000

Model 1: English ability effects on Math Achievement

Source	Sum of Squares	Df	Mean Square		Number of obs =    2108 F(1,  2106) =  321.37
Model	14921.361	1	14921.361		Prob> F  =  0.0000
Residual	97781.3687	2106	46.4298997		R-squared     =  0.1324
Total	112702.73	2107	53.4896676

Math Score	Coefficient	Std Err.	T	P>|t|
OLDS	.1421757	.0079309	17.93	0.000
Constant	12.39079	.3248009	38.15	0.000

Model 2: SES effects on Math Achievement

Source	Sum of Squares	Df	Mean Square
Model	25008.6541	1	25008.6541
Residual	87694.0755	2106	41.6401118
Total	112702.73	2107	53.4896676

Math Score	Coefficient	Std Err.	T	P>|t|
SES	4.872712	.1988298	24.51	0.000
Constant	19.59027	.1629372	120.23	0.000

Model 3: Socioeconomic Status and English ability effects on Math Achievement

Source	Sum of Squares	Df	Mean Square		Number of obs =   2108 F(2,  2105) =  344.23
Model	27776.0744	2	13888.0372		Prob> F =  0.0000
Residual	84926.6553	2105	40.3452044		R-squared =  0.2465
Total	112702.73	2107	53.4896676

Math Score	Coefficient	Std Err.	T	P>|t|
OLDS	.0698275	.0084311	17.85	0.000
SES	3.984045	.2231973	8.28	0.000
Constant	16.6781	.3864713	43.15	0.000

Please respond to the following questions

3) What proportion of variance is explained by Model 2?

4) Write the regression equation of Model 3 and explain each of its parts. No need to describe results yet.

5) Based on Model 3, compute the standardized slopesfor SES and English ability; interpret them, and specify what additional information is learned from the standardized slopes that cannot be learned from the unstandardized slopes.

6) Describe in one or two paragraphs the importance of using multiple regression analysis(instead of only using bivariate regression) for studying the relationship between children's language ability and math score. What additional information is learned from multiple regression that cannot be learned from the simple bivariate regression?

7) Explain in two paragraphs the main results of Model 3.