Download Name - Mr. Nickels

Name: _____________________________
Mr. Nickels
Date: _____________
Math 3C
Regressions Packet
1) The accompanying table shows the enrollment of a preschool from 1980 through 2000.
Write a linear regression equation to model the data in the table.
2) A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to
the number of blocks, x, the cottage is from the beach. The accompanying table shows a
random sample of sales and location data.
A. Write a linear regression equation that relates the price of a cottage to its distance
from the beach.
B. Use the equation to predict the price of a cottage, to the nearest dollar, located three
blocks from the beach.
3) Jean invested $380 in stocks. Over the next 5 years, the value of her investment grew, as
shown in the accompanying table.
A. Write the exponential regression equation for this set of data, rounding all values to
two decimal places.
B. Using this equation, find the value of her stock, to the nearest dollar, 10 years after
her initial purchase.
4) The accompanying table shows the percent of the adult population that married before
age 25 in several different years. Using the year as the independent variable, find the
linear regression equation. Round the regression coefficients to the nearest hundredth.
Using the equation found above, estimate the percent of the adult population in the year
2009 that will marry before age 25, and round to the nearest tenth of a percent.
5) Which scatter diagram shows the strongest positive correlation?
6) A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the
coins that land heads up are returned to the box, and then the process is repeated. The
accompanying table shows the number of trials and the number of coins returned to the
box after each trial.
A. Write an exponential regression equation, rounding the calculated values to the
nearest ten-thousandth.
B. Use the equation to predict how many coins would be returned to the box after the
eighth trial.
7) In a mathematics class of ten students, the teacher wanted to determine how a homework
grade influenced a student’s performance on the subsequent test. The homework grade
and subsequent test grade for each student are given in the accompanying table.
A. Give the equation of the linear regression line for this set of data.
B. A new student comes to the class and earns a homework grade of 78. Based on the
equation in part a, what grade would the teacher predict the student would receive on the
subsequent test, to the nearest integer?
8) The relationship of a woman’s shoe size and length of a woman’s foot, in inches, is given in the
accompanying table.
The linear correlation coefficient for this relationship is
(1) 1
(3) 0.5
(2) –1
(4) 0
9) The population growth of Boomtown is shown in the accompanying graph.
If the same pattern of population growth continues, what will the population of Boomtown be in
the year 2020?
(1) 20,000
(3) 40,000
(2) 32,000
(4) 64,000
10) Which graph represents data used in a linear regression that produces a correlation coefficient
closest to –1?
11) The table below shows the results of an experiment that relates the height at which a ball is
dropped, x, to the height of its first bounce, y.
A. Find x , the mean of the drop heights.
B. Find y , the mean of the bounce heights.
C. Find the linear regression equation that best fits the data.
D. Show that ( x , y ) is a point on the line of regression. [The use of the grid is optional.]
12) What could be the approximate value of the correlation coefficient for the accompanying
scatter plot?
(1) -0.85
(3) 0.21
(2) -0.16
(4) 0.90
13) The table below, created in 1996, shows a history of transit fares from 1955 to 1995. On
the accompanying grid, construct a scatter plot where the independent variable is years.
State the exponential regression equation with the coefficient and base rounded to the
nearest thousandth. Using this equation, determine the prediction that should have been
made for the year 1998, to the nearest cent.
14)
X
-2
-4
-8
-9.3
F
2
5
2
7
A) Median: __________
B) Mode: __________
C) Mean: __________
D) Standard Deviation: __________
E) Sample Deviation: __________
15) In a certain school district, the ages of all new teachers hired during the last 5 years are
normally distributed. Within this curve, 95.4% of the ages, centered about the mean, are
between 24.6 and 37.4 years. Find the mean age and the standard deviation of the data.
16) The national mean for verbal scores on an exam was 428 and the standard deviation was
113. Approximately what percent of those taking this test had verbal scores between 315
and 541?
(1) 68.2%
(3) 38.2%
(2) 52.8%
(4) 26.4%
17) A set of normally distributed student test scores has a mean of 75 and a standard
deviation of 6. Determine the probability (as a fraction) that a randomly selected score
will be between 69 and 82.