Causation
SECONDARY 1 MATH
Causation
when a change in one variable creates a direct change in the other variable
it is related to correlation in that we see causation when we have strong or
perfect correlation between the two variables
Causation vs. Correlation
Cause & Effect
Correlation
If you paint, you create a painting
If you paint, you might sell a painting
If you stand in the rain without
protection, you get wet
If you stand in the rain you may
get struck by lightning
In the 1990s, researchers found a strong positive relationship between the number of television sets per person x and the life expectancy y of the citizens in different countries. That is, countries with many TV sets had higher life expectancies.
Does this imply causation?
NO
By increasing the number of TV’s in a country, can we increase the life expectancy
of their citizens?
NO
Are there any hidden variables that may explain this strong positive correlation?
Medical Care
Technology Access
Higher Average Income
Diet
TV Advertisements/Information
Leisure Time
This figure shows the correlation between several countries with their per capita chocolate consumption and the number of Nobel Prize winners per 10 million population.
Will eating more chocolate cause
your country to win more Nobel Prizes?
In the past people noticed that sick people often smelled bad, and they assumed that bad smells caused disease. Are bad smells and disease an example of causation?
No, what they didn’t realize at the
time was that germs cause bad smells and germs also cause disease
Bad smells and disease are correlated but one does not cause the other
Aura is taking her friends to the movies for her birthday. There is a strong positive relationship between the number of movies tickets she buys and the amount of money she spends.
Is it reasonable to assume causation in this situation?
YES
As Aura increases the number of movie tickets she purchases, does this cause
her to spend more money?
YES
Would the correlation coefficient in this situation be 1? Explain
Not necessarily, if the prices of some tickets are different it would not be a perfectly linear relationship
A local university is keeping track of the number of art students who use the pottery studio each day.
Write the equation of the linear regression line for the
situation
A local university is keeping track of the number of art students who use the pottery studio each day.
What does the slope tell us about the story?
It appears that 1.18 fewer students are using the
pottery studio each day
A local university is keeping track of the number of art students who use the pottery studio each day.
What does the y-intercept tell us about the story?
We would predict that the day before the university
started keeping track there would have been 20.43
students that used the pottery studio
A local university is keeping track of the number of art students who use the pottery studio each day.
Using the regression equation, predict how many students
will use the pottery studio on day 13.
5.09 students using
the studio on day 13
A local university is keeping track of the number of art students who use the pottery studio each day.
Identify the correlation coefficient for this situation
strong negative correlation
Identify the correlation coefficient for this situation