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Name: ________________________
Regression Review Homework
1) The table below shows the number of new stores in a
coffee shop chain that opened during the years 1986 through
1994.
a) Using
to represent the year 1986 and y to represent
the number of new stores, write the exponential regression
equation for these data. Round all values to the nearest
thousandth.
b) Using your equation from part a, determine the number of
new stores for the year 2000?
c) During which year did the number of stores first exceed
2500 stores?
2) The data collected by a biologist showing the growth of a colony of bacteria at the end of
each hour are displayed in the table below.
a) Write an exponential regression equation to
model these data. Round all values to the
nearest thousandth.
b)
b) Assuming this trend continues, use this equation to estimate, to the nearest
ten, the number of bacteria in the colony at the end of 7 hours.
3) Since 1990, fireworks usage nationwide has grown, as shown in the accompanying table, where t
represents the number of years since 1990, and p represents the fireworks usage per year, in
millions of pounds.
a) Find the equation of the linear regression model for this set of data, where t is the independent
variable. Round values to four decimal places.
b) Using this equation, determine in what year fireworks usage would have reached 99 million
pounds.
c) Based on this linear model, how many millions of pounds of fireworks would be used in the
year 2008? Round your answer to the nearest tenth.
4) Water is draining from a tank maintained by the Yorkville Fire Department. Students measured the
depth of the water in 15-second intervals and recorded the results in the accompanying table.
a) Write the power regression equation for this set
of data, rounding all values to the nearest ten
thousandth.
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
b) Using this equation, predict the depth of the water
at 2 minutes, to the nearest tenth of a foot.
o)
5) Which graph represents data used in a linear regression that produces a correlation coefficient
closest to ?
1)
2)
3)
4)
6) As shown in the table below, a person’s target heart rate
during exercise changes as the person gets older. Which value
represents the linear correlation coefficient, rounded to the
nearest thousandth, between a person’s age, in years, and that
person’s target heart rate, in beats per minute?
1)
2)
3) 0.998
4) 1.503
7) The points in the scatter plot below represent the ages of automobiles and their values. Based
on this scatter plot, it would be reasonable to conclude:
1) Age and value have a coefficient of
correlation that is less than zero.
2) Age and value have a coefficient of
correlation that is equal to zero.
3) Age and value have a coefficient of
correlation that is between zero and 0.5.
4) Age and value have a coefficient of
correlation that is greater than 0.5.