Basic HTML Version
Q
uantitative
R
easoning &
P
roblem
S
olving
340
© 2014 Pacific Crest
Step
Explanation
8.
Find the slope
The slope of the regression equation is
y
x
m r
σ
σ
=
, where
σ
x
is the standard
deviation of the x-values,
σ
y
is the standard deviation of the y-values, and r
is the correlation coefficient.
y
x
σ
σ
=
=
=
14.981
0.738
2.003
5.517
m r
9.
Find the y-intercept
Calculate the y-intercept of the linear regression equation using the formula
y = mx + b because (x, y) must be on the line. The point (x, y) lies on the
regression equation. Substitute those values into y = mx + b and solve for
b.
y
= m
x
+ b
72.9412 = 2.003(10.7647) + b
b = 51.379
10. Find the linear
regression
equation
Create the linear regression equation in the form of y = mx + b and then
substitute any value for x that is in the range of x values used to build the
linear regression equation.
y
= m
x
+ b
linear regression equation:
y
= 2.003
x
+ 51.379
Use this equation to determine the test score for
a student who scores 17 on the quiz (x = 17):
y
= 2.003(17) + 51.379
y
= 85.43; the student is most likely to score 85.43 on the test.
11. Validate
Compare the calculation results to your original approximation of the linear
regression equation to determine reasonableness of the slope, intercept,
and the correlation coefficient. Also use a second tool for verifying results.
Our approximate equation was:
y
= 3
x
+ 34
The slope 3 is actually close to calculation of 2 while the intercept of 34 is also close
to the calculation of 51. Checking the correlation coefficient through the calculator
online gives a result for
r
of 0.7378, the same value we found.
(Note that when you
generate a scatterplot in Excel, you can elect to have the linear regression equation
show, as well as
r
2
.)