Homework 4 Solutions

Ch. 10: 

9.  (a) 21%  (b) 65%  (c) 50%  (d) 50%

Work for (a).  This student was 1.65 SDs below average on the midterm.
He should be at about 0.8 SDs (r x 1.65 = 0.5 x 1.65) below avg on the
final.  The percentile rank on the final then comes out to about 21%.


Ch. 11:

4.  (a)  rms error = (1 - r^2)^0.5 x SD of final scores = 12

    (b) 65.8 - This student is 30/25 = 1.2 SDs above avg on the
midterm, and should be above avg on the final by r x 1.2 = 0.72 SDs;
this is 10.8 points.

    (c) 12, the rms error: see part (a).  It is OK to use the rms
error inside a strip because the diagram is football-shaped.

5.  (a) about 5%

    (b) New avg is about 65.8, new SD is 12.   (80-65.8)/12 is about 1.18
The answer is about 12%.


Ch. 12:

1.  In a run of 1 SD, the regression line rises r x SD.  The slope is
0.60 x 20/10 = 1.2 final points per midterm point.  The intercept is
55 - 1.2 x 70 = -29.  so the equation is
   predicted  final score = 1.2 x midterm score - 29

7.  The slope has to be 0.5, because the regression line has to go
through the point of averages.