Exhibit 14-1 To comply with recent Federal legislation, school districts must study their students' growth as a whole, as well as the achievement of various subgroups of students. Over a 3-day period, students are assessed on their reading achievement, science and math knowledge, and social studies skills and these results are combined into a global "composite" score. To analyze the increase in this global score from the Freshman year to the Sophomore year, the model y = α + β1x1 + β2x2 + e was fit to a sample of student data. (The actual data contained categorical variables for each ethnic subgroup. To simplify the analysis, only the African American / White categorical variable is included here.)
y = growth in composite score (Soph. - Fresh. score)
x 1 = last year's composite score
x 2 = 1 if a student is African American, 0 if white
x 3 = 1 if a student receives free or reduced price lunch (a measure of socio-economic status), 0 if not
The computer output from the regression analysis is shown below.

-Refer to Exhibit 14-1. a) Is the Model Utility test significant at the .10 level? Explain your reasoning, referring to specific information in the computer output.
b) Calculate the estimated mean growth in composite score for white students who scored 280 as Freshmen and who are receiving free/reduced lunch.

Question

Exhibit 14-1 To comply with recent Federal legislation, school districts must study their students' growth as a whole, as well as the achievement of various subgroups of students. Over a 3-day period, students are assessed on their reading achievement, science and math knowledge, and social studies skills and these results are combined into a global "composite" score. To analyze the increase in this global score from the Freshman year to the Sophomore year, the model y = α + β1x1 + β2x2 + e was fit to a sample of student data. (The actual data contained categorical variables for each ethnic subgroup. To simplify the analysis, only the African American / White categorical variable is included here.)
y = growth in composite score (Soph. - Fresh. score)
x 1 = last year's composite score
x 2 = 1 if a student is African American, 0 if white
x 3 = 1 if a student receives free or reduced price lunch (a measure of socio-economic status), 0 if not
The computer output from the regression analysis is shown below.

-Refer to Exhibit 14-1. a) Is the Model Utility test significant at the .10 level? Explain your reasoning, referring to specific information in the computer output. 
b) Calculate the estimated mean growth in composite score for white students who scored 280 as Freshmen and who are receiving free/reduced lunch.

Quizplus · Accepted Answer

The Answer of Exhibit 14-1 To comply with recent Federal legislation, school districts must study their students' growth as a whole, as well as the achievement of various subgroups of students. Over a 3-day period, students are assessed on their reading achievement, science and math knowledge, and social studies skills and these results are combined into a global "composite" score. To analyze the increase in this global score from the Freshman year to the Sophomore year, the model y = α + β1x1 + β2x2 + e was fit to a sample of student data. (The actual data contained categorical variables for each ethnic subgroup. To simplify the analysis, only the African American / White categorical variable is included here.)
y = growth in composite score (Soph. - Fresh. score)
x 1 = last year's composite score
x 2 = 1 if a student is African American, 0 if white
x 3 = 1 if a student receives free or reduced price lunch (a measure of socio-economic status), 0 if not
The computer output from the regression analysis is shown below.

-Refer to Exhibit 14-1. a) Is the Model Utility test significant at the .10 level? Explain your reasoning, referring to specific information in the computer output. 
b) Calculate the estimated mean growth in composite score for white students who scored 280 as Freshmen and who are receiving free/reduced lunch.

Exhibit 14-1 to Comply with Recent Federal Legislation, School Districts