can be found in many situations. It can also be graphed and analyzed in several ways. This lesson will focus on how to analyze data
that has been input into your calculator. As a review, we will also look at graphs of data
as seen on the calculator screen. This lesson assumes that you already know how to put data
into your calculator. If you do not know how to do this and need help click here
Consider the following example.
Ten 25-year olds were surveyed to find out their years of formal education (first grade – college) and their annual income. The data
is presented below.
|Years of Education ||8||10||12||12||13||14||16||16||18||19|
|Income (in thousands) ||18||19||24||25.5||26.6||28||30||33||40||45|
In most cases, it is useful to look at a graph
of the data. Once you have put the years of education data
in L1 and the income data
in L2, you want to see a graph
of the data. This is done on the calculator by having the calculator graph
you get the screen which turns on statistical graphs or plots.
This screen indicates that all four of the plots are turned off. To turn
on Plot 1, press
and set up your screen to match the one below.
You have the option of either setting your window by hand or by having the calculator help you by pressing
. If you use the ZoomStat option, you should see the screen below.
Many times, after data
has been graphed, we want to see if there is a function
(usually a line) that will explain
the data. This line
can be called a trend line, since it can be used to explain
trends in the data. It can also be called a line
of best fit. In statistics, it is referred to as the line
of best fit or the regression line. All of these names simply mean
that we are trying to find a line
to help us describe the relationship between our data. In this case, we are trying to describe the relationship between the years of education and annual income. It makes sense that your education level is a determining factor
in how much money you make.
To find this line
to describe the relationship between education and income, we need to use the
button and choose the CALC menu. From the CALC menu, we will use option 4:LinReg(ax+b).
When you press
, you should see the LinReg(ax+b) command on your screen as shown below.
The calculator needs to know which two sets of data
to use in order to find the trend line. Since our data
is in L1 and L2, that’s what we will enter into the calculator. L1 and L2 are the 2ND function
keys of the 1 and 2 keys. So, you need to press:
Not only would we like the calculator to find a trend line
for us, we want to graph
also. Remember that in order to graph
anything, we must have something in Y=. To have the calculator put our line
into Y1, we need the following keystrokes:
Now when you press
the calculator will show the numbers for the trend line
and put that equation
into Y1 for you.
Notice that my calculator has been set to two decimal places. If your calculator did not show r and r2
there is a way to get them to appear on the screen. First let’s look at the trend line
and then we will work with r and r2
The screen you see (regardless of the r and r2
values) is telling you that the line
that describes the relationship between education and income is y=2.37x-3.73
. That equation
is in Y1 and can be graphed along with the data
points by simply pressing
We can now use that trend line
to predict the annual income of someone with 15 years of formal education. We just substitute 15 for x in our equation
So it is reasonable to expect someone with 15 years of formal education to make approximately 31,820. (Remember that the data
was given in thousands of dollars.)
This trend line
we now have is very useful for making predictions about someone’s annual income. However, we have to be careful not to go too far away from our original data. The line
that we found describes the data
we put into the calculator. Data
that is too far away from our original numbers will not be as accurate.
Now what can we do if your calculator did not show r and r2
. Use the following procedure:
to get the CATALOG menu. Then use the
repeatedly until you see DiagnosticOn. Then press
You will now have to redo the regression command, but you should now see r and r2
on your screen.
Now that we have r and r2
, let’s talk about what they mean.
The r value is what is known as a correlation coefficient. It is a number to tell how well the straight line fits the data. The closer the r value is to +1 or –1, the better the line fits the data. As the r value gets closer to 0, the worse the fit gets. In our case, the r value of .96 means that our line is a very good fit to our data.
The r2 value is found just by squaring the r value. In statistics, the r2 value describes how much of the variation in the data is accounted for by the trend line. It is a very interesting topic, but also fairly complicated to understand. If you are interested in further statistical analysis of data, see your statistics teacher.
You should now be able to input data, graph
it, find the trend line
it with the data, use the trend line
to make a prediction, and find the r and r2
values for the line. These skills will be very useful to you not only in your math class, but also in your science class, or anywhere you deal with data
collection and analysis.