HELLO, I am Mr. Tarrou.
Today we are going to be looking at scatter plots in Statistics.
Now scatter plots will be the first graph that we take a look at the displays two quantitative
pieces of data or is a bivariate graph.
Instead of maybe you are doing quality control at the end of the assembly line and you are
looking for how many grams of something are in an item, or you just looking at that one
variable.
That is when you look at stem plots, box plots, and histograms when you are looking at just
one variable.
Now we are going to look at two.
The example you are going to see here in a minute, since this is about school, we are
going to look at hours of study per week and gpa.
And we are going to compare those two variables.
I am just going to make the numbers, but again, the idea of the structure of a scatter plot.
So a scatter plot and correlation, I thought I was going to fit more notes up here.
We won't really speak much about correlation in this video.
But I will mention it.
Again, we are dealing with two quantitative variables.
We are looking for any observable pattern that shows that there is a relationship between
two variables.
Now whether that really means the variable on the x axis is causing the change on the
y, that would be nice if we could show it, but that is not always necessary.
We just want to use scatter plots to make predictions.
Use those x values to predict values of y.
And it does not necessarily, and most of the time there will not be a cause and effect
relationship.
We can only run statistics analysis on linear patterns.
So when we draw a scatter plot with our calculator or by hand, if it does not follow a linear
pattern we can talk about what we see and whether it is positive association or negative
association.. and maybe the points are scattered all over the place... or a horizontal line
where there is no association.
But if it is linear, and this only intro to statistics so we are limited to only being
able to run math calculations on linear patterns.
Again just because it is Intro to Statistics.
If you have a clear explanatory and response variable, explanatory will go on the x axis
and the response will go on the y axis.
Alrighty then!
So you got that copied?
And this is just a structure, sort of an outline of topics that are in this section.
You definitely are going to have some more notes and you will definitely want to look
at those examples in your book so you have a clear idea of what you are going to be doing.
When there is no clear explanatory and response variable, then it does not really matter what
you put on the x or y axis.
Just put whatever you want where you want it.
But again, if you think there might even be a change that one variable is helping to explain
why the other is changing, or why the y values are changing, put the explanatory on the x
axis.
Patterns...
Again we are going to be hoping to see a pattern in our scatter plots so that we can use our
x's to predict our y values.
Ok.
Great!
[laughing] We will not be using the language of independent and dependent because we are
trying to emphasize how hard it is to prove cause and effect.
We are pretty convinced now that smoking does cause lung cancer, but for a long time it
was just...
there is evidence of that.
Because people that smoke might drink more, have different life style like what they do
for work, or how much they make for year for health care and such.
So cause and effect is a very very hard thing to prove.
So we want to avoid any kind of language that falsely implies that x is causing the change
in y unless we can actually prove that.
That is difficult and will not really be discussed in this video.
A pattern in a scatter plot shows that there is just some relationship which could just
be coincidence.
But if there is a relationship, if there is a pattern whether it straight, whether it
is curved...
Like maybe it looks exponential growth.
If there is a pattern in the scatter plot, then we can use the values of x to predict
the values of y.
So even though it could be just coincidence, it is still going to be useful.
And again, I am going to say this word correlation, but I did not fit it on the board and I don't
think I am going to fit it into 15 minutes exactly what correlation is.
We will be talking about that in a later video.
But correlation does not mean causation.
Just because you see a pattern in a scatter plot, even if it is perfectly straight, you
will not be able to say that the x is causing the change in y.
Now, its like running track.
I have to change the camera.
So... [nananananana] Alrighty then:)
Now here I am going to just make up a couple of quick examples of scatter plots and show
some relationships.
Now we would hope that how much study will improve your gpa.
And as a reminder quantitative data only on the x and y axis.
You can make something that looks like a scatter plot with maybe a categorical variable on
the x axis, but by definition it is not.
Only x and y variable can be quantitative, no categorical.
Let's just say that we assume that the more you study the higher your gpa will be.
Well clearly there is a limit to high your gpa can get.
If you have a 3.9 you have to study a lot to get a 4.0.
So I am going to guess that this pattern will not actually be linear.
Maybe it kind of tapers down as you increase the hours of studying.
And then a couple of times, we always have those kids like I have got a couple right
now that hardly study at all but yet their grades are just phenomenal.
And you will have some students that will study a lot and not really have very much..
or very good gpa's.
So the pattern might not be very tight, but there could be and probably will be an overall
upward trend of those values.
Ok.
And I think it is pretty reasonable to think that the hours you study is going to effect
your gpa.
Well ok.
Let's just super briefly, I will do a calculator video to help show you how to do this in your
calculator.
But let's say that all of these blue dots represent females.
Ok.
What if I do want to display...
um...
categorical variables in my scatter plot.
What if I want to compare the work with the women to the men?
How could I put that categorical variable into the scatter plot?
Well with your calculator the hours and the gpa are probably going to be in list one and
list two, and since I just did an example of women's work ethic and gpa, maybe I want
to put the men in as an orange dot.
Well, in a calculator if you are not doing this by hand, what you will do is in list
3 put some more hours in and in list 4 put some gpa's in.
Now make two scatter plots at once.
Plot one for the women and plot two for the men, and display those on the same screen.
Then put a different mark or different color, maybe you can look at some kind of comparison.
I am laying these on top because I don't really think your gender is going to effect your
gpa or your work ethic... or the relationship between these two.
But you can display those different marks or colors inside the scatter plot to display
categorical variables in that scatter plot.
But remember, the x and the y axis must be quantitative.
We will do a nice calculator video to remind you, or show you actually, how to create these
scatter plots.
Now you're amount of studying is not the only thing that effects your gpa.
You know, it is your intelligence, or maybe how much pressure you get at home to do one
or the other... or probably both.
So it kind of makes sense that how much you study will effect your gpa, but let's say
that we notice that we make a scatter plot and we compare the temperature...
or excuse me...
Let's not do that.
We are going to compare how much money is made selling ice cream to how many people
come into the hospital complaining some kind of cold.
So frequency of colds.
Kind of a stupid example, right.
But let's say that we notice that the more ice cream is being sold the higher this value
gets, and in a certain region like maybe in a grocery store .... So zero dollars to a
couple dollar hundred dollars if you are talking about a little stand's sales per day or something
like that.
Kind of a ridiculous example, but I just want to say what if we did notice that in an area
the higher the ice cream sales were, the lower the frequency of colds.
Kind of like a stupid sounding example.
Well that brings in the idea of lurking variables.
When you have an x and y variable, one variable on the x axis and one on the y axis, there
might be a direct link between those two variables.
This is very hard to prove.
Now you have two types of lurking variables that can be causing that relationship to show
up.
There is a common response lurking variable and a confounding lurking variable.
My previous example I erased, maybe a confounding lurking variable would be not only is your
hours studying effecting your gpa but also just your general IQ level.
Well, both of those are going to effect your gpa, the response.
Now in this ridiculous example I am talking about between ice cream sales and whether
or not people are getting colds, what cold be actually causing this relationship?
This might actually be valid.
And in my mind it kind of makes sense.
What would drive up ice cream sales and what season of the year do people get fewer colds?
Would that be summer?
So in this example there could very well be a common response lurking variable of just
the temperature.
And the temperature could be driving up the heat, could be driving up ice cream sales
and at the same time, you know, not that many people are getting sick.
Well, great!
I just gave you a reasonable example of a lurking variable that would follow this kind
of relationship.
But you know what I can still do?
I can still use the ice cream sales to predict how much..
or how many people are going to a clinic or the hospital for a cold.
SO!
Scatter plots, you are going to be making plenty of them.
You are going to be looking for relationships in there.
There may be causation, or there may not be because there is a lurking variable in the
back ground.
But if there is a pattern, then we can use the x's to predict the y values.
WHOO!
Alright, one more page of notes and I have less than five minutes.
[nanananana] Alrighty then.
Here we go.
Last page for this video.
So...
BAM!
Alright.
Interpreting scatter plots.
When you look at a scatter plot and you want to tell your teacher the or the person your
grading your AP test what do you see, make sure you hit these points.
And again this is an outline of topics and concepts, not an actual example.
But you want to talk about the form.
What do you see?
Is the pattern linear, is it curved, or are there just some cluster of points.
Maybe you are comparing the SAT scores from the south and the north and you might notice
a cluster from those two regional areas in your scatter plot.
Direction and strength.
Does it have a positive association or a negative association?
In other words is the slope positive or is the slope negative?
What is the strength?
Now students will remember strength as the strength... or how tightly the points follow
a line because it is Intro to Stats and we cannot talk about patterns that are linear
or at least crunch numbers on it.
But the real definition of strength is how closely the points follow a clear pattern.
So even if the pattern is curved, if they are perfectly in line with that curve the
strength is very very high.
We will not measure strength unless it is linear.
Are there any outliers?
Well if you have a scatter plot, and I am trying to just draw this ellipse to represent
a collection of points.. in this case linear points...
If within that data range of x have a point that is vertically above or below all of the
other ones, that would be marked as an outlier.
An outlier is still a point that falls far outside the pattern.
No outlier is good, but the ones that are horizontally way outside the pattern...
those are even more of a bad thing.
They are even more influential.
Neither one of these outliers are good.
Lines are not resistant.
They use the mean in their calculation.
You will see that in the formulas in the next video, but the outliers in the vertical direction
do not change the slope or the y intercept as the outliers in the horizontal direction.
So this just validates or repeats what I just said.
So when interpreting scatter plot: Form, Direction, and Strength, and Outliers.
I really should have four bullets.
Form, direction, strength, and outliers.
I think my 15 minutes are almost up.
Please read your book.
Read those examples.
Watch my later videos when I actually finish this lesson and show you how to use your calculator.
Thank you very very much for watching.
I know there are a lot of these out there.
I do appreciate you choosing my videos.
BAM!