In this video we'll take a look at how
to find predicted scores or predicted
values in multiple regression and
finding predicted values is really very
helpful because if we can get an
understanding of what a predicted value
is that will really help to unlock many
of the features of multiple regression
we can better understand what's going on
with a number of different measures
including for example our R squared
what a residual is which we'll talk
about in another video and so on
it really does help quite a bit so let's
go and take a look at this here on your
screen you see an equation and this
equation says y hat equals a plus b1
times x1 + b2 times x2 and then here y
hat is equal to the predicted value for
an observation
so in other words what is the actual
value that we get in terms of predicting
y or our dependent variable or criterion
variable as a direct result of our
regression analysis so what is our
regression analysis predict for the
dependent or criterion variable and a is
known as the y-intercept and
mathematically that's just the value of
y hat when all the exes are 0 so in
other words if you look at this and this
x10 here and this x10 here then
multiplying that out that would just be
y hat equals a as these terms would just
become 0 so that's why the y-intercept
is defined as the value of y hat when
all x is 0 and then b1 and b2 are what
are referred to as the unstandardized
regression coefficients for in this case
since we have to the first and second
predictors respectively
x1 x2 are the score scores on the first
and second predictors respectively so
s80 score of 1200 that's rx1 and then
the social support score of 62 that's
rx2 here so we could run the regression
analysis in SPSS and we get a table of
output but i've gone ahead and done that
here and you can see it right here the
coefficient stable this is the table
that we want to use to get the values
for our equation to find a predicted
score and we'll go ahead and do this in
a little while run this again and show
you how I got this just to be complete
but in this analysis i went ahead and
adjust to the decimal places so that
they will be output to five decimal
places and that's not always necessary
but when I have very small values like
notice this is point zero zero 172 this
is basically two one-hundredths this is
1 1001 that small it can be helpful to
carry them out to more decimal places in
order to get an accurate predicted score
but in many cases are variables are
independent variables are predictors get
these B values that are much larger than
this and we don't to be as concerned
about carrying them out beyond the
standard default of two decimal places
but when they're small like this I like
to do that for accuracy
so here's our equation once again why
had equals a plus B 1 x1 + b2 x2 and my
constant is the a so points0 3238 notice
that goes right here and then the b1 is
the capital B he run standardized
coefficients
for my first predictor which is s80
score so I have points0 0172 so that's
why you see this right here and then
that's x SI t score and that is the
actual score that an individual got on
the s80 and then my next understands
coefficient is for social support and
that's points0 2164 so that's why you
see that here and then that's x the
individuals social support score so now
that we have the basic equation let's go
ahead and solve one on our own so here
notice for the first person they got a
1200 on the s80 and their social support
score was 62 so we use that equation
that we saw a minute ago and here it is
once again and then we plug in 1,200
here for satc since that's there is a
t-score and 62 for social support since
that's the social support score and when
we do that we find the following so
here's our equation once again and
notice here now I have the 1200 plugged
in and the 60 to plug in as well and
that works out to a predicted score a
3.43 806
so in other words using the predictors
s80 score and social support using those
independent variables we get a predicted
GPA value of about 3.44 if we rounded to
two decimal places here and notice the
actual GPA is 3.45 so we have a value
that was very close this is called 3.44
and the axles 3.45 so our regression
analysis our regression equation got
very close to the actual value we got
three-point-four for once again and the
actual value is 3.45 so we're only off
by point zero one and that's very good
and that's actually that won't be the
case using this equation for all of
these values the s80 and social support
scores if we plug all of these in and
got predicted values they all wouldn't
be that close because that really is
quite outstanding but many will be
closed some will be further away and our
r squared for this problem
the bigger the r-squared the closer is
21 recall that indicates the amount of
variance r squared the amount of
variance that's accounted for in the
dependent variable from the predictors &
R R squared is big
that means we're counting for a lot of
variance in the dependent variable or in
college GPA in this case so the bigger
the r-squared the more variance we count
for the bigger the r-squared overall on
average the closer these predicted
values will be to the actual values
ok so if you're r squared is very large
these predictive values will be very
close to the actual values if you r
squared is low or small then the
predicted values will tend to be further
away from the actual values so the
better these predictors do at predicting
college GPA of the dependent variable
the higher the r square and likewise the
closer are actual predictive values will
be to the values on the dependent
variable