* Show your work, you can get points for good procedures.

* Four sections to work on

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), which was 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? Hint: You need to do some computations/calculations

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.