Problems 415
- The following data indicate the gain in reading speed versus the number of weeks
in the program of 10 students in a speed-reading program.
Speed Gain
Number of Weeks (wds/min)
221
342
8 102
11 130
452
557
9 105
785
562
790
(a) Plot a scatter diagram to see if a linear relationship is indicated.
(b) Find the least squares estimates of the regression coefficients.
(c) Estimate the expected gain of a student who plans to take the program for
7 weeks.
- Infrared spectroscopy is often used to determine the natural rubber content of
mixtures of natural and synthetic rubber. For mixtures of known percentages, the
infrared spectroscopy gave the following readings:
Percentage 02040 60 80100
Reading .734 .885 1.050 1.191 1.314 1.432
If a new mixture gives an infrared spectroscopy reading of 1.15, estimate its
percentage of natural rubber.
- The following table gives the 1996 SAT mean math and verbal scores in each
state and the District of Columbia, along with the percentage of the states’ gradu-
ating high school students that took the examination. Use data relating to the
first 20 locations listed (Alabama to Maine) to develop a prediction of the mean
student mathematics score in terms of the percentage of students that take the
examination. Then compare your predicted values for the next 5 states (based on
the percentage taking the exam in these states) with the actual mean math scores.