LAMC
Yun
Math 137 Test 2 Module 3-4
_____
Last name________________________________
10/29/2014
First name__________________________
You may use a calculator but not a cellphone, tablet or an iPod. Please clearly mark your choices
on multiple choice questions and box your answers on free response questions.
1. (6 pts.) Each research question below describes a relationship between two quantitative
variables. Choose the variable that should be plotted on the horizontal X-axis.
(a)
How is the age of a teenager related to the average number of text messages they send
and receive each day?
response variables
(b)
weight
average number of text messages
For women aged 25-35 what is the relationship between their annual salary and the
number of years of education?
salary
2.
age
age
years of education
lurking variable
(6 pts.) These scatterplots show body measurements for 34 adults who are physically active.
Some measurements are a “girth” which is a measure of length around a body part.
(a) The form of the relationship between bicep girth and weight is
linear
curvilinear
neither
(b) The association between bicep girth and weight is
positive
negative
neither
(c) For this sample of adults, which variable has a stronger relationship to weight?
bicep girth
thigh girth
same
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3. (6pts.) Below is the data from 21 female college students. Forearm length in inches is the
explanatory variable. Height in inches is the response variable. The line is a good summary of
the linear pattern in the data.
(a) Based on the graph of this line which is the best prediction of the height of a woman with a
forearm of 11 inches?
64.5 inches
68 inches
68.75 inches
just under 70 inches
(b) The equation of this line is: Predicted height = 39 + 2.7*forearm length. Use this equation to
predict the height of a woman with a 10 inch forearm.
4. (4 pts.) Two students conduct a study to investigate the relationship between forearm length
and height. Maria measures the subjects in centimeters. In a scatterplot of the data she sees a
linear relationship between the variables, so she calculates the correlation coefficient. She
determines that r = 0.86. John measures the same subjects in inches. He also calculates the
correlation coefficient. What do you expect the correlation will be for John’s measurements?
John’s Correlation will be approximately 0.86(.61) = 0.52 because one centimeter = 0.61
inches
John’s correlation will be approximately 0.86 because the pattern in the data will be the
same.
John’s correlation will be approximately r = 1 because there is a strong relationship
between John’s measurement and Maria’s measurement.
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5. (8pts.) At Los Medanos College a statistics instructor posted the following information on her
office door at the end of the semester:
Final course grades have not been posted. Karen wants to predict her final exam score based
on this information. She has an 82 pre-final exam average. Find the equation of the leastsquares line and use the equation to predict for Karen’s final exam score.
s
Use the formulas:
y =a + bx
br y
a  y  bx
sx
6.
(5 pts.) Match the equation to the graph.
3
7. (8 pts.) Match each Scatter plot to the residual plot.
8. (5 pts.)
9. (3 pts.)
4
10. (6 pts.) The regression line for predicting a variable y is found to be y  1  3x . Calculate the Standard
Error Se 
SSE
for the following data:
n2
x
3
4
6
7
10
y Prediction
9
13
15
24
32
(Error)2
Error
11. (3 pts.) Choose the most likely correlation value for this scatter plot.
12. (8pts.) A researcher has collected data on the price of gasoline from 1990 to 2010 and has
found that the price in dollars after t years can be predicted using the equation:
y  0.0128x 2  .3584 x  1.90
(a) Using this model predict the price of gas 1998?
(b) Based on the equation, what year had the most expensive gas?
(c) How much did gas cost in that year?
5
13. (6pts.) The population in a small city is growing at a rate of 3.2% every year. If there are
15,000 people living in the city now.
(a) Write an exponential equation for the population after t years
(b) Use our equation to predict the population after 8 years.
14. (6pts.) Given y  2000(.9722) x ,
(a) State the initial y value.
(b) Find the rate of decrease
15. (5pts.) Write the number of the correct equation next to each graph:
16. (6pts.) Write the standard form of quadratic equation with vertex (1,2) that passes through
(2,-1).
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17. (6pts.) The scatterplot below shows Olympic gold medal performances in the long jump from
1900 to 1988. The long jump is measured in meters.
(a) For the regression line predicted long jump = 7.24 + 0.014 (year since 1900), what does the
slope of the regression line tell us?
A.
B.
C.
D.
Each year the winning Olympic long jump performance is expected to increase 7.24
meters.
Each year the winning Olympic long jump performance is expected to increase
0.014 meters.
Each time the Olympics are held (generally every four years), the long jump gold
medal winner will definitely achieve a 0.014 meter increase over the previous gold
medal winner.
Each time the Olympics are held (generally every four years), there is a predicted
1.4% increase in long jump performance.
(b) For the regression line predicted long jump = 7.24 + 0.014 (year since 1900), what does the
7.24 tell us?
A.
B.
C.
D.
7.24 meters is the predicted value for the long jump in 1900.
7.24 meters is the actual value for the long jump in 1900.
7.24 is the minimum value for the long jump from 1900 to 1988.
7.24 meters is the predicted increase in the winning long jump distance for each
additional year after 1900.
18. (3pts.) Which of the following is NOT true of a least-squares regression line?
A.
B.
C.
D.
The least-squares regression line is chosen so that the sum of the squares of the
residuals is as small as possible.
The least-squares regression line is the only line with the smallest sum of the
squares of the errors.
The sum of the squares of the residuals is always equal to r2.
If all the points are on a line, then the sum of the squares of errors is zero.
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