In this example the dependent variable is the GPA a student receives (termgpa) for a specific
semester and the independent variable is the percent of his or classes that were attended
(atndrate.)
The scatter plot of the data looks like this.
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Linear Regression
te rm gpa = 0.62 + 0.02 * atndrat
R-Square = 0.31
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25.00
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75.00
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atndrate
As you can see, there is a positive linear relationship, but the correlation is not very strong
since the points do not follow the line very closely. In the output, you are given an R2 = 0.31.
The square root of this is r = 0.56. We call this value the correlation coefficient.
From SPSS we can also get the descriptive statistics for termgpa and atndrate:
Descriptive Statistics
N
TERMGPA
ATNDRATE
Valid N (listwise)
680
680
680
Minimum
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6.25
Maximum
4.00
100.00
Mean
2.6010
81.7096
Std. Deviation
.73659
17.04699
The line that is fit through these points is the regression line. We can find the equation of this
line from these equations:
s
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yˆ  b0  b1 x
b0  y  b1 x
b1  r  y 
s
x
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Since our y is termgpa and our x is atndrate,
b1  .56 .737
 .024
17.05
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b0  2.601  .024(81.710)  .62
We can actually run the regression in SPSS and get the same results:
Coeffi cientsa
Model
1
(Const ant)
ATNDRATE
Unstandardized
Coeffic ients
B
St d. Error
.625
.115
.024
.001
St andardiz ed
Coeffic ients
Beta
.560
t
5.443
17.590
Sig.
.000
.000
a. Dependent Variable: TERMGPA
The (Constant) row gives us b0, which is just a little off due to rounding error.
The ATNDRATE (our x variable) row gives us b1.
So our regression line is termˆ gpa  .625  .024(atndrate) .
In this example, the b0 could be interpreted as the expected GPA for the semester if you
attended 0% of your classes.
Also, b1 can be interpreted as the expected increase in GPA for a unit (1%) increase in class
attendance.
Lastly, we can test to see if the linear relationship between attendance rate and semester GPA
is significant. i.e. H0: β1=0 vs. Ha: β1≠0. We use a t-test for this. The t statistic is t =
b1
.024
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 17.59 (notice the round off error). This is given in the SPSS output along with
se(b1 ) .001
the p-value of .000. Thus, we reject the null hypothesis and conclude that there is a significant
linear relationship between class attendance rate and semester GPA.
When doing this test, make sure to look at the line for the x variable, not for the constant!