# Projection Model

Projection models are used to predict scores in a future grade and are meant to answer the question “Given this student’s observed past scores and based on patterns of scores in the past, where is she likely to score in the future?”

The projection model is a variant of linear regression where an equation is established that relates students’ past scores to their future scores. The projection model is flexible in that multiple past scores, as well as other measures, can be used to predict a single future score.

For example, a grade 10 ACT Plan Mathematics score can be predicted based on grade 9 ACT Explore scores in all four subject areas (English, mathematics, reading, and science) and on the number of months between the two assessments:

• ACT Plan Mathematics Score= β0 + β1 × ACT Explore English Score + β2 × ACT Explore Mathematics Score + β3 × ACT Explore Reading Score + β4 × ACT Explore Science Score + β5 × Months Elapsed

In this model, the β values are weights relating each input variable to the future test score. We refer to these weights as projection parameters.

The projection model we employ is different from the conditional score average model because, instead of conditioning on a single past test score, we are conditioning on multiple past test scores. Generally, score predictions from the projection model are more accurate than score predictions from the conditional score average model because it uses more information for predicting future test scores.

Below, we provide projection parameters for several pairs of assessments. Find the assessment pair and select the growth period you are interested in to download the projection parameters.

Test 1Test 2Growth Period
ACT ExploreACT ExploreGrade 8 to grade 9 (10–14 months)
ACT ExploreACT PlanGrade 8 to grade 10
ACT ExploreACTGrade 8 to grade 11
ACT ExploreACT PlanGrade 9 to grade 10 (10–14 months)
ACT ExploreACT QualityCore English 96–12 months
ACT ExploreACT QualityCore Algebra I6–12 months
ACT ExploreACT QualityCore Geometry6–12 months
ACT ExploreACT QualityCore Biology6–12 months
ACT ExploreACT QualityCore English 1018–24 months
ACT ExploreACT QualityCore Geometry18–24 months
ACT ExploreACT QualityCore Biology18–24 months
ACT PlanACT PlanGrade 9 to grade 10 (10–14 months)
ACT PlanACTGrade 10 to grade 11 (10–14 months)
ACT PlanACTFall grade 10 to spring grade 11
ACT PlanACT QualityCore English 106–12 months
ACT PlanACT QualityCore Geometry6–12 months
ACT PlanACT QualityCore Algebra II6–12 months
ACT PlanACT QualityCore Biology6–12 months
ACT PlanACT QualityCore U.S. History6–12 months
ACT PlanACT QualityCore English 1118–24 months
ACT PlanACT QualityCore Geometry18–24 months
ACT PlanACT QualityCore Algebra II18–24 months
ACT PlanACT QualityCore US History18–24 months
ACT PlanACT QualityCore Chemistry18–24 months
ACT PlanACT QualityCore Pre-Calculus18–24 months
ACTACT Compass Writing Skills10–14 months
ACTACT Compass Pre-Algebra10–14 months
ACTACT Compass Algebra10–14 months
ACTACT Compass College Algebra10–14 months
ACTACT Compass Reading Skills10–14 months

### How to Apply the Projection Model

In this example, 131 students took the ACT Plan assessment in 10th grade and then took the ACT test in 11th grade (11 or 12 months later). Students’ predicted ACT scores are determined by their ACT Plan scores in all four subject areas, as well as the number of months elapsed between the ACT Plan and ACT tests.

Predicted ACT scores can be compared to actual ACT scores to obtain residual scores that measure growth relative to peers. The predicted values and residual scores are highlighted in the spreadsheet.

The worksheet named “Projection Model Parameters” is obtained from the ACT Plan/ACT/Grade 10 to grade 11 (10–14 months) row in the table above.