Review Mod 3 KEY – You should look over all CW, HW, Notes, and checkpoint quizzes.
Do this review on a separate piece of paper and staple it to this!
1. In 1998, Ann bought a house for $184,000. In 2009, the house is worth $305,000.
Find the average annual rate of change in dollars per year of the value of the house.
Round your answer to the nearest cent. Let x represent number of years after
1990
Write the data provided into two ordered pairs, Find the slope, include the appropriate
label, and interpret the meaning of the slope, Find the equation of the line representing
Ann’s house value, Then, Estimate Ann’s house value in 2004
305,000−184,000
Points used: (8, 184,000) & (19, 305,000), 𝑚 =
= 11,000. The average annual
19−8
rate of change is $11,000 per year. This tells us that for each year that passed, from
1998 to 2009, Ann’s house increased in value by an average of $11,000. The equation for
this prediction value of Ann’s house is 𝑉 = 11,000𝑥 + 96,000 where x is the number of years
after 1990. We would estimate Ann’s house value to be $250,000 in 2004 by plugging in
x=14 into the prediction equation. This is a valid prediction since it lies within our range of
data and would not be an extrapolation.
2. Given the following scatterplots:
a. List the graphs’ correlation from least to greatest 4, 2, 3, 1
b. Which graph has the strongest linear correlation Plot 4
c. Which graph has the strongest non-linear correlation Plot 2
d. The four correlation coefficients for the scatterplots shown are -0.1169,
0.7699, -0.9396, and 0.1632. Match the correlations to the plots.
Plot 1: 0.7699, Plot 2: -0.1169, Plot 3: 0.1632, Plot 4: -0.9396
3. Does a strong positive correlation PROVE that they depend on each other? Does it
always show that a relationship exists? Can you come up with an example that it
doesn’t?
We can never say it proves, we can only say that the data suggests or the data
supports this conclusion. It does not always show that a relationship exists, you can
have a low correlation like in plot 2 from the previous problem, but it has a strong
nonlinear relationship.
4. For an essay question, what key things should you talk about?
You should talk about the direction, form, strength, outliers. The first sentence
should be what the graph is portraying. Then you should talk about what the data is
suggesting, what this means, and who would benefit from knowing this information.
5. How do you choose which is the explanatory variable and which is the response
variable?
The explanatory variable is X (input), the response is Y (output). To choose, time is
always the explanatory, if that is an option. If time is not one of the variables, we
start to ask ourselves “does one influence the other one?” or “is one a response to
the other one?”, and make our decision that way.
6. For what values can we use our regression line to predict?
We can only predict for x values between the lowest value for the explanatory and
the highest, otherwise we would be extrapolating. Remember that extrapolation is
used in real life, so that we can predict the future, but it may or may not be
reliable since there tends to be large amounts of error in such predictions. If you
do extrapolate, you must make a note of your prediction as extrapolation and would
not be reliable. You may not calculate the prediction and just state that this would
be extrapolation and should not do it.
7. What are the four things to describe a linear scatterplot? direction, form,
strength, outliers
8. Find the least squares regression line
Be sure to be able to give me the EQUATIONS for the m and b, from the notes,
then coming up with the equation of the line, again from your notes.
Match each description of a set of measurements to a scatterplot. Then describe
what a dot represents in each graph.
9.
x = average outdoor temperature and y = heating costs for a residence for 10
winter days Scatterplot 3
10. x = height (inches) and y = shoe size for 10 adults Scatterplot 1
11. x = height (inches) and y = score on an intelligence test for 10 teenagers
Scatterplot 2
12. Regression Lines. Give the equations for slope and y intercept of a regression line.
y  mx  b Where
mr
sy
sx
b  y  mx
13. For the following data:
a) Make a scatter plot. (x,y) on graph paper
x
2
4
6
8
10
12
14
15
y
3
4
8
11
13
14
18
17
b) Draw a line of fit for your scatter plot, find the equation of the line
Your equation should be similar to y = 1.175x + 0.571, but doesn’t need to be
exact since you did it by hand. Select 2 points on your line (not points from the
data as your line may not hit any of the data points) and use those to calculate a
prediction equation for the data.
c) Use your equation to predict y for x = 13 y = 15.846
14. What does an outlier do to an r-value? Explain in complete sentences and say how
will the r-value change, increase or decrease?
If an outlier is placed into a data set, the r value will get closer to zero, because
the data is not as strong linearly. This does not mean that the r-value will be
necessarily close to zero, just that it will shift in that direction. If a data point is
placed close to the pattern, the correlation coefficient would get closer to one or
negative one, depending on what the direction is.