MI-2 – Sample Exam 2
6 March 2017
Name: __________________
Mod: _____
1. Suppose that we are given a linear model 𝑊 = 5.49𝐻 − 220 which relates the weight of
a university student (in pounds) to their height (in inches).
a. Interpret the slope of this linear model.
b. Interpret the y-intercept of this linear model.
c. (*) Suppose that we got this model as a linear regression from a data set where the
minimum height of a student collected was 60 inches, and the maximum height
was 75 inches. Explain why this linear model might not give a good prediction of
a student who is 80 inches tall.
2. Suppose that we know that we have two quantities 𝐻 and 𝑃 which are related
quadratically. Fill in the rest of the table below based on this assumption.
H
P
Δ𝑃
Δ2 𝑃
Δ3 𝑃
3
4
10
5
6
–2
3
3. Consider the system of equations:
z  2
 3x  5 y 

y  2z 
1
 4x 
6 x  10 y  2 z  0

a. Explain why matrix algebra fails to solve this system.
b. Use Gaussian elimination on your calculator to determine how many solutions
this system has. Provide a brief justification for your answer.
Linear Thinking
S17
4. Consider the following data set which gives the population P (in millions of people) t
years after 1790:
t (years after
1790)
P (millions of
people)
t (years
after 1790)
P (millions
of people)
0
10
20
30
40
3.9
5.2 7.2
9.6
12.9 17.0 23.2 31.4 38.6 49.4 63.0
140
150
50
160
60
70
170
80
180
90
190
100
110
120
130
200
76.2
92.2
106.0 123.2 132.2 151.3 179.3 203.2 226.5 248.7
a. What is a good window to view this data in a scatterplot on your calculator?
b. Find the linear regression line and check the correlation (corr) and the 𝑅 2
coefficients you get from doing a linear regression. What does this seem to imply
about your linear model?
c. Is your linear regression line a good model? Explain briefly.
Linear Thinking
S17
5. Three construction companies are ordering materials. Company A needs to get wood
concrete, and steel for their buildings. They need 100 tons of material total for all their
construction projects. Company B needs twice as much concrete and steel (each), but half
as much wood as Company A for 162.5 tons total. Company C forgoes the use of wood,
and needs the same amount of concrete and three times the amount of steel that Company
A needs for 155 tons total.
a. Define the variables you want to use in this situation.
b. Set up a system for this problem and its associated matrix equation. Then solve
with whatever method you please and state your answer in sentences.
6. (Challenge) Suppose we have an arithmetic sequence 𝑎𝑛 . What can you say about the
sequence
𝑏
+ 𝑎𝑛 if 𝑛 > 1
𝑏𝑛 = { 𝑛−1
4
if 𝑛 = 1
Linear Thinking
S17