Question 1: Howard Weiss, owner of a musical instrument distrib-utorship, thinks that demand for bass drums may be related to the number of television appearances by the popular group Stone Temple Pilots during the previous month. Weiss has collected the data shown in the following table:
Demand for Bass Drums 3 6 7 5 10 7
Stone Temple Pilots' 3 4 7 6 8 5
TV Appearances:
a) Graph these data to see whether a linear equation might describe the relationship between the group's television shows and bass drum sales.
b) Use the least-squares regression method to derive a forecasting equation.
c) What is your estimate for bass drum sales if the Stone Temple Pilots performed on TV nine times last month?
d) What are the correlation coefficient (r) and the coefficient of determination (r2) for this model, and what do they mean?
Question 2: Thirteen students entered the business program at Hillcrest College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Hillcrest program for 2 years.
Student A B C D E F G
SAT Score 421 377 585 690 608 390 415
GPA 2.90 2.93 3.00 3.45 3.66 2.88 2.15
Student H I J K L M
SAT Score 481 729 501 613 709 366
GPA 2.53 3.22 1.99 2.75 3.90 1.60
a) Is there a meaningful relationship between SAT math scores and grades?
b) If a student scores a 350, what do you think his or her GPA will be?
c) What about a student who scores 800?