EPSY 8269: Matrix Algebra for Statistical Modeling
Vector Assignment 3
Consider the following scores on Quiz 1 and Quiz 2, each are out of a possible 15 points.
Student
1
2
3
4
5
6
7
8
9
10
11
12
Quiz 1
13
15
9
11
6
12
10
11
13
10
9
14
Quiz 2
14
14
10
10
7
7
9
9
13
9
10
13
Complete the following tasks to conduct Orthogonal Decomposition of one vector for Bivariate
Regression. To complete these tasks, use deviations scores instead of raw scores.
Hint: convert the raw score vectors to deviation score vectors and proceed.
1. Suppose we wanted to predict performance on Quiz 2 (Y) from performance on Quiz 1 (X).
Represent geometrically, the partitioning of the sums of squares of y on an orthogonal
coordinate graph.
2. Now compute the partitioning of the sums of squares by employing the Pythagorean
Theorem:
[L(dY)]2 = [L(pYX)]2 + [L(pYE)]2 
3. Compute R2.
SST = SSR + SSE