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Math 137 Unit 4 and 5 Review
1)
2)
3) Investigating explanatory variable:
4)
5) Match the equation to the graph:
6)
The Consumer Report ratings for breakfast cereals have a fairly strong negative linear relationship
with the grams of sugar per serving. The least-squares regression line is:
Predicted rating = 60 – 2.4*sugar
Which of the following is a valid interpretation of the slope?
a) A one-point increase in Consumer Reports ratings corresponds to a predicted decrease of 2.4
points is the grams of sugar in a serving.
b) A one-gram increase in sugar per serving corresponds to a predicted decrease of 2.4 points in
the Consumer Reports rating.
7) Match each Scatter plot to the residual plot:
8)
9)
10)
11)
12)
13) When comparing the linear relation between the price of gas and the number of miles people drive in
a week, the correlation coefficient r = .82. What does the value of r2 tell us about these variables?
14) (Review Question)
a) Between 10 and 12
b) 13
c) Between 16 and 18
15) The following scatterplot show the relationship between the sales of CD’s versus the sales of LP
vinyl records (in millions) over the years 1983-2000. Three models are shown. The following
scatterplots, r 2 , and standard errors examine the three equations. Based on the values of r 2 and SE,
which model is the best fit? Explain your reasoning by interpreting r 2 and SE in context.
A. Linear Model
SE=103.0428, r 2  0.8818
B. Quadratic Model
SE=34.7384, r 2  0.9871
C. Exponential Model
SE=74.30405, r 2  0.7749
16) Find the percent increase or decrease for each of the following:
a) 𝑦=2000(1.12)x
b) y=2000(1.03)x
c)𝑦=2000(1.003)x
d) y=2000(.82)x
e) 𝑦=2000(.956)x
f) 𝑦=2000(.12)x
17) The initial number of bacteria in a sample is 150,000 and it grows at a rate of 2% every day.
a) Write an exponential equation for the number of bacteria after t days.
b) Use your equation to predict the number of bacteria after 15 days.
18) A group of scientists observed a population of birds in a remote area and counted the birds in 1998. After
returning every year and counting the birds, they came up with the following formula for the number of
birds: 𝑦=12000×(.84)t.
a) How many birds used to live in the area in 1998?
b) Predict the population in 2010.
19) A researcher has collected data on the price of gasoline from 1992 to 2014 and has found that the
price in dollars after t years can be predicted using the equation: y = − 0.0256t2 +0.3584t +1.90
a) According to this model what was the price of gas in1990?
b) Using this model predict the price of gas 1998?
c) Based on the equation, what year had the most expensive gas?
d) How much did gas cost in that year?
20. The following ordered pair data and scatterplot describe the grams of fat in a meal and the number of
calories.
r = 0.969 SE = 52.3
Variable
Fat
Calories
Mean
37.5
618
StDev
16.74
206.8
a) Use the above information to write a regression line.
b) Describe the association (if any) between calories and fat in a meal.
c) Write a sentence interpreting the meaning of the correlation coefficient, r.
d) Write a sentence interpreting the meaning of the slope for the meal.
e) Write a sentence interpreting the meaning of the y-intercept for the meal.
f) Write a sentence interpreting the meaning of r2 for the meal.
g) Write a sentence interpreting the meaning of the standard error, Se.
h) Predict the number of calories in a meal with 37 grams of fat, if applicable.
i) Predict the number of calories in a meal with 85 grams of fat, if applicable.
j) It was found that the residual plot has no pattern. What does this tell us about this linear model?
21. For which explanatory data values are we allowed to make predictions for (in linear and curvilinear
models)?