Data & Analytics Exam > Data & Analytics Videos > Statcrunch Tutorials for Beginners > Working with StatCrunch: Bivariate (or Simple) Regression
Working with StatCrunch Bivariate (or Simple) Regression Video Lecture
Text Transcript from Video
Hi, my name is Bart Poulson and in this tutorial,
I'm going to show how to use StatCrunch to
do bivariate regression, uh, a way of looking
at the relationship between two quantitative
variables in this case. Um, the first thing
you'll need to do is go to statcrunch.com
and then you'll need to log into your account.
I assume you already have one. I'm going to
use a data set that already exists. So, I'm
gonna come up here to "Explore" to "Data"
and I'm gonna to use a data set, uh, that's
called "yms Table 1.15" because it's from
a uh published statistics book. Um, when I
search for that one, up comes this picture
of a high school, and the data set consists
of information on states, one row per state.
It gives the population, the average SAT verbal
and math scores, percent taking, no high school
diploma, teacher pay, and if I broaden that
out a little bit, you can see is teacher pay,
average teacher pay in thousands of dollars,
the region, and the population percentage
over 65. Ok. Good. Um, what I'm going to do
is I'm going to look at the association between
teacher pay in thousands of dollars and SAT
math scores, uh, the averages for both states.
I already did this as a correlation coefficient
and as a scatterplot, but right now I'm gonna
take it one step further and look at the regression
equation as well as a scatterplot with a regression
line through it. The way to do that in StatCrunch
is to come over here to "Stat," click on that,
and come down to "Regression." And for this
one I'm gonna do what's called "Simple Linear."
"Simple" means I'm using one predictor variable,
teacher salary in this case, and one outcome
variable, average SAT math scores, in this
case. It's called "linear" because it's going
to draw a straight line through the scatterplot
and it's going to assess how well the data
fit that straight line and what the slope
and intercept of that straight line is. Now
it's possible to do regression with other
shapes, uh, of curves and what not, but—and
it's actually not that difficult. You usually
do what's called a transformation of the data
to work on that, but we may cover that another
time, but not right now. Any case, I'm going
to use "Stat," "Regression," "Simple Linear."
And when I get there, I'm going to select
my x-variable—that's the one that I
want to use as a predictor. In this case,
I going to use, um, "Teacher Pay" in thousands
of dollars, um, as my predictor. And as the
outcome, I'm going to look at SAT Math scores.
I'm not gonna do any restrictions or combination
variables, so I'm gonna skip to the next one.
Um, I'm not interested in these right now.
I may talk about those another time. I hit
the "Next" box. The one that is really important
is this one right here: Plot the fitted line.
That will give me a scatterplot with a straight
regression line through it. Now, all the rest
of these can be very, very important as what
are called diagnostic charts to see if you
meet the assumptions of, uh, simple linear
regression—things like linearity, and
normality, and, uh, presence of outliers and
what not. But again, I'm not gonna worry about
those right now. Um, this is just in case
I want more than one output on a page. I don't,
so I hit "Calculate." And great. Now what
it does is it brings up two pages and I'm
gonna talk about both of 'em. The first one
right here is the actual statistical results,
it's the numbers, but to put it into a perspective,
I'm gonna come down here and hit "Next" to
go to the scatterplot first. Now, I uh—In
a previous tutorial, I did a correlation coefficient,
which is the number, and I also did a scatterplot,
uh, this exact same picture for these variables.
The only difference here is that this one
has a regression line that runs through it.
Well, the other difference is that I'm not
able to change the, uh, labels and the titles
on this one, but I do get the regression line.
So you can see that strangely it's a downhill
relationship. That is, in states where teachers
are paid more, there's also a lower average
SAT score. Uh, it's a difference of probably
45 points from the lowest to highest paid
states. So, it's not huge, but it is enough
to matter. Any case, what I'm gonna do now
is now that I have the picture, the scatterplot
with the negative line through it, I'm gonna
look at the actual numbers behind the relationship.
This tells me that I'm doing simple linear
regression. My dependent variable is the outcome
variable, the thing that I'm trying to predict.
In this case it's average SAT math scores
for the state. The independent variable means
the one that I'm using as the predictor, in
this case, teacher pay in thousands of dollars.
Now, as—as a little note, the terms
independent and dependent variable are from
experimental research where you have a manipulated
independent variable and a dependent variable
which is seen as the effect or the result
of that causal variable. In this case, that's
not true, so it would be more accurate to
simply label these as "predictor" and "outcome."
I wish they would do that, uh, because those
terms are also easier to understand, but,
you know, there you have it. This line right
here is the actual regression equation and
what it tells us is that the average SAT math
score for a state, uh, the predicted value,
is equal to 611.998—that is, give each
state that value for its SAT math score. And
then, for each step up in teacher pay in thousands
of dollars, subtract 2 points from the average
SAT score for that, uh, state. Sample size
is 51. That'd be the 50 states plus Washington
DC. The correlation coefficient between these
two is negative 3773, and if you were to go
back to an earlier one and look at the correlation
matrix I—I did, you would see that
number there. Uh, perhaps a more important
one, right here, is this one, is the r2, is
simply the square of this correlation coefficient.
But the r2, uh, which sometimes is called
the coefficients of determination, or more
often the proportion of variants accounted
for, um, is—the r2 is a nice indication
of the strength of the relationship. The advantage
to this is that correlation coefficients,
the one that's right here, are not linear.
A .4 is not twice as strong as a .2. You have
to square them. You get .16 and .4. So, it's
actually 4 times as strong. Um, the r2 is
probably the best way to compare, uh, statistical
output in relationships. Anyhow, in this case,
it tells us that if we know teacher pay, we
can account for, or predict 14% of the variants
in average SAT math scores for our 51 localities.
Down here at the parameter estimates, you'll
see that this 611.998 is the same one that's
up here. It's simply the intercept, the y-intercept
for the line. The slope, which indicates the
change in average SAT scores for each change
step in teacher pay, is -.20 so on, which
is the same number that's right here. Now
one additional thing that we wanna look at
is this number here on the side. This is called
the P-Value. This indicates this is a null
hypothesis significance test for each coefficient.
This one right here tells us that it's extremely
unlikely that the intercept of 611 is due
to random error if we assume that the true
intercept is zero, but you know, with SAT
scores, that's not possible, so that's not
a big deal. The one that's probably more important
is the slope which is this number—the
2089 so on—where the P-Value is 0063.
The rule here is if P-Values are less than
05, then that indicates that there is a low
probability of getting something like this
through random sampling when there is in fact
no effect, or the coefficient is 0 in the
population. Anyhow, this lets us know that
the negative coefficient is a reliable number.
Um, this 63 down here is also the, uh, probability
value for the entire equation, but because
there's only one predictor variable, this
and this are the same value. And I think that
for, uh, the relationship between two quantitative
variables between, again, teacher pay in thousands
of dollars and SAT math scores, so we've now
established what the scatterplot looks like,
that it does fit a downhill straight line,
we have the regression equation for it, and
that's probably enough for right now.
I'm going to show how to use StatCrunch to
do bivariate regression, uh, a way of looking
at the relationship between two quantitative
variables in this case. Um, the first thing
you'll need to do is go to statcrunch.com
and then you'll need to log into your account.
I assume you already have one. I'm going to
use a data set that already exists. So, I'm
gonna come up here to "Explore" to "Data"
and I'm gonna to use a data set, uh, that's
called "yms Table 1.15" because it's from
a uh published statistics book. Um, when I
search for that one, up comes this picture
of a high school, and the data set consists
of information on states, one row per state.
It gives the population, the average SAT verbal
and math scores, percent taking, no high school
diploma, teacher pay, and if I broaden that
out a little bit, you can see is teacher pay,
average teacher pay in thousands of dollars,
the region, and the population percentage
over 65. Ok. Good. Um, what I'm going to do
is I'm going to look at the association between
teacher pay in thousands of dollars and SAT
math scores, uh, the averages for both states.
I already did this as a correlation coefficient
and as a scatterplot, but right now I'm gonna
take it one step further and look at the regression
equation as well as a scatterplot with a regression
line through it. The way to do that in StatCrunch
is to come over here to "Stat," click on that,
and come down to "Regression." And for this
one I'm gonna do what's called "Simple Linear."
"Simple" means I'm using one predictor variable,
teacher salary in this case, and one outcome
variable, average SAT math scores, in this
case. It's called "linear" because it's going
to draw a straight line through the scatterplot
and it's going to assess how well the data
fit that straight line and what the slope
and intercept of that straight line is. Now
it's possible to do regression with other
shapes, uh, of curves and what not, but—and
it's actually not that difficult. You usually
do what's called a transformation of the data
to work on that, but we may cover that another
time, but not right now. Any case, I'm going
to use "Stat," "Regression," "Simple Linear."
And when I get there, I'm going to select
my x-variable—that's the one that I
want to use as a predictor. In this case,
I going to use, um, "Teacher Pay" in thousands
of dollars, um, as my predictor. And as the
outcome, I'm going to look at SAT Math scores.
I'm not gonna do any restrictions or combination
variables, so I'm gonna skip to the next one.
Um, I'm not interested in these right now.
I may talk about those another time. I hit
the "Next" box. The one that is really important
is this one right here: Plot the fitted line.
That will give me a scatterplot with a straight
regression line through it. Now, all the rest
of these can be very, very important as what
are called diagnostic charts to see if you
meet the assumptions of, uh, simple linear
regression—things like linearity, and
normality, and, uh, presence of outliers and
what not. But again, I'm not gonna worry about
those right now. Um, this is just in case
I want more than one output on a page. I don't,
so I hit "Calculate." And great. Now what
it does is it brings up two pages and I'm
gonna talk about both of 'em. The first one
right here is the actual statistical results,
it's the numbers, but to put it into a perspective,
I'm gonna come down here and hit "Next" to
go to the scatterplot first. Now, I uh—In
a previous tutorial, I did a correlation coefficient,
which is the number, and I also did a scatterplot,
uh, this exact same picture for these variables.
The only difference here is that this one
has a regression line that runs through it.
Well, the other difference is that I'm not
able to change the, uh, labels and the titles
on this one, but I do get the regression line.
So you can see that strangely it's a downhill
relationship. That is, in states where teachers
are paid more, there's also a lower average
SAT score. Uh, it's a difference of probably
45 points from the lowest to highest paid
states. So, it's not huge, but it is enough
to matter. Any case, what I'm gonna do now
is now that I have the picture, the scatterplot
with the negative line through it, I'm gonna
look at the actual numbers behind the relationship.
This tells me that I'm doing simple linear
regression. My dependent variable is the outcome
variable, the thing that I'm trying to predict.
In this case it's average SAT math scores
for the state. The independent variable means
the one that I'm using as the predictor, in
this case, teacher pay in thousands of dollars.
Now, as—as a little note, the terms
independent and dependent variable are from
experimental research where you have a manipulated
independent variable and a dependent variable
which is seen as the effect or the result
of that causal variable. In this case, that's
not true, so it would be more accurate to
simply label these as "predictor" and "outcome."
I wish they would do that, uh, because those
terms are also easier to understand, but,
you know, there you have it. This line right
here is the actual regression equation and
what it tells us is that the average SAT math
score for a state, uh, the predicted value,
is equal to 611.998—that is, give each
state that value for its SAT math score. And
then, for each step up in teacher pay in thousands
of dollars, subtract 2 points from the average
SAT score for that, uh, state. Sample size
is 51. That'd be the 50 states plus Washington
DC. The correlation coefficient between these
two is negative 3773, and if you were to go
back to an earlier one and look at the correlation
matrix I—I did, you would see that
number there. Uh, perhaps a more important
one, right here, is this one, is the r2, is
simply the square of this correlation coefficient.
But the r2, uh, which sometimes is called
the coefficients of determination, or more
often the proportion of variants accounted
for, um, is—the r2 is a nice indication
of the strength of the relationship. The advantage
to this is that correlation coefficients,
the one that's right here, are not linear.
A .4 is not twice as strong as a .2. You have
to square them. You get .16 and .4. So, it's
actually 4 times as strong. Um, the r2 is
probably the best way to compare, uh, statistical
output in relationships. Anyhow, in this case,
it tells us that if we know teacher pay, we
can account for, or predict 14% of the variants
in average SAT math scores for our 51 localities.
Down here at the parameter estimates, you'll
see that this 611.998 is the same one that's
up here. It's simply the intercept, the y-intercept
for the line. The slope, which indicates the
change in average SAT scores for each change
step in teacher pay, is -.20 so on, which
is the same number that's right here. Now
one additional thing that we wanna look at
is this number here on the side. This is called
the P-Value. This indicates this is a null
hypothesis significance test for each coefficient.
This one right here tells us that it's extremely
unlikely that the intercept of 611 is due
to random error if we assume that the true
intercept is zero, but you know, with SAT
scores, that's not possible, so that's not
a big deal. The one that's probably more important
is the slope which is this number—the
2089 so on—where the P-Value is 0063.
The rule here is if P-Values are less than
05, then that indicates that there is a low
probability of getting something like this
through random sampling when there is in fact
no effect, or the coefficient is 0 in the
population. Anyhow, this lets us know that
the negative coefficient is a reliable number.
Um, this 63 down here is also the, uh, probability
value for the entire equation, but because
there's only one predictor variable, this
and this are the same value. And I think that
for, uh, the relationship between two quantitative
variables between, again, teacher pay in thousands
of dollars and SAT math scores, so we've now
established what the scatterplot looks like,
that it does fit a downhill straight line,
we have the regression equation for it, and
that's probably enough for right now.
About this Video
Apr 29, 2026 Last updated
Related Exams
Video Description: Working with StatCrunch: Bivariate (or Simple) Regression for Data & Analytics 2026 is part of Statcrunch Tutorials for Beginners preparation. The notes and questions for Working with StatCrunch: Bivariate (or Simple) Regression have been prepared according to the Data & Analytics exam syllabus. Information about Working with StatCrunch: Bivariate (or Simple) Regression covers all important topics for Data & Analytics 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Working with StatCrunch: Bivariate (or Simple) Regression.
Introduction of Working with StatCrunch: Bivariate (or Simple) Regression in English is available as part of our Statcrunch Tutorials for Beginners for Data & Analytics & Working with StatCrunch: Bivariate (or Simple) Regression in Hindi for Statcrunch Tutorials for Beginners course. Download more important topics related with notes, lectures and mock test series for Data & Analytics Exam by signing up for free.
Description
Video: Working with StatCrunch: Bivariate (or Simple) Regression of Statcrunch Tutorials have been curated by the Data & Analytics experts, helping you revise the topic quickly for exam preparation. Watch on EduRev.
Information about Working with StatCrunch: Bivariate (or Simple) Regression
Here you can find the meaning of Working with StatCrunch: Bivariate (or Simple) Regression defined & explained in the simplest way possible. Besides explaining types of Working with StatCrunch: Bivariate (or Simple) Regression theory, EduRev gives you an ample number of questions to practice Working with StatCrunch: Bivariate (or Simple) Regression tests, examples and also practice Data & Analytics tests.
Related Searches
Previous Year Questions with Solutions, Sample Paper, pdf , Semester Notes, Working with StatCrunch: Bivariate (or Simple) Regression, Viva Questions, practice quizzes, video lectures, Important questions, MCQs, Working with StatCrunch: Bivariate (or Simple) Regression, Objective type Questions, mock tests for examination, shortcuts and tricks, Extra Questions, Free, Working with StatCrunch: Bivariate (or Simple) Regression, ppt, Exam, study material, Summary, past year papers;