Name: _________________________________________ Pd: 1 2 3 4 6 7 Date: 11/11/15
[Unit 3 –System of Equations + ACP Review: Lesson 2]
2
Association vs. Causation and Linear Regression
Goal! : SWBAT compare and contrast association and causation in real-world problems and write equations of
best-fit lines with technology to make predictions.
Causation
The event that occurs when a change in one variable
a change in another variable. It can really only be determined from data
collected from a
.
Also known as
Association variables, either
or
. An observed relationship between two
.
Shark attacks vs. monthly ice cream sales in summer months
SCENARIO
EXPLANATION (Coincidence or not?)
As ice cream sales increase, the rate
of shark attacks increases sharply.
Therefore, increase in ice cream
sales causes shark attacks since
consuming ice cream makes people
tastier to sharks.
The example shows a correlation but fails to recognize the importance of time
in relationship to ice cream sales. Ice cream is sold during the summer months
at a much greater rate, and it is during the summer months that people are
more likely to engage in activities involving water, such as swimming. The
increased shark attacks are simply caused by more exposure to water-based
activities, not ice cream.
Bottom Line: Correlation does not necessarily mean Causation.
1.
2.
Which statement can be concluded about the data?
A Studying more hours causes fewer missed
problems.
B There is a negative correlation between the
number of hours studied and the number of
questions missed.
C Studying causes great test scores.
D There is a causation but not a correlation
between hours studied and the number of
questions missed.
Independent Practice Complete ____/9
Decide whether the situation illustrates Association or Causation. Write A or C and explain why.
Real-World Scenario
A or C / Why?
1. A survey showed that sleeping with the light on was positively associated
to nearsightedness.
2. A controlled experiment showed a positive association between the
number of cigarettes smoked and the probability of developing lung cancer.
A – you tell why
C
3. A random sample of students found that owning a cell phone had a
negative association with riding the bus to school.
4.
A
Jason concluded that more pools are caused by hotter
weather. This is incorrect for what reason?
A The data shows no correlation.
B The relationship could be related to outside factors,
such as the cost of building pools.
C There is causation but no correlation between the
variables.
D The graph shows that higher temperatures cause
fewer pools to be build.
5. Megan and Bryce opened a new store called the Donut
Pit. Their goal is to reach a profit of $20,000 in their
18thmonth of business. The table and scatterplot
below represent the profit, P, in thousands of dollars,
that they made during the first 12 months, t.
(a) Use linear regression to find the equation that best
models the data. (round to the nearest hundredths)
Equation = P = 0.57t + 2.33
(b) Use your equation to predict whether Megan and
Bryce will reach their goal in the 18th month of their
business. No, when t = 18; P ≈ 12.59
(c) Calculate and interpret the correlation coefficient.
r = 0.95; strong positive correlation
6.
7. Use the table below to determine the slope for
the data? m = 4.86
Free
Throws
Points
Scored
Use your calculator to find the equation of the trend line
for the data. Equation = Y = -0.48x + 140.09
3
4
4
5
5
6
6
7
7
8
9
30
25
35
30
35
41
48
45
50
49
55
What does the slope mean for this situation?
Average points per free throws allowed per game
Calculate and interpret the correlation coefficient.
r = -0.75; moderately negative correalation
8. Which of the following values of r would indicate a
weak positve linear correlation?
F r = -0.91
H r = 0.06
G r = -0.51
J r = 0.45
9. The table shows the total career homeruns for a
player at the end of each seaon.
Predict the total number of career home runs after the
2017 season. y = 22.4x – 45043.9; In 2007, 137 hours