we know that
The residual value is the observed value minus the predicted value.
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]
where
Predicted value.--> the predicted value given the current regression
equation
Observed value. --> The observed value for the dependent
variable
find the residuals value
point 1)
(2, 94.5)
yˆ=−6x+105.7
for x=2
Observed value=94.5
Predicted value=-6*2+105.7-----> 93.7
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE
so
RESIDUAL VALUE=[94.5-93.7]----> 0.8-----> 1
point (2,1)
point 2)
(3, 89)
yˆ=−6x+105.7
for x=3
Observed value=89
Predicted value=-6*3+105.7-----> 87.7
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE
so
RESIDUAL VALUE=[89-87.7]----> 1.3-----> 1
point (3,1)
point 3)
(4,80)
yˆ=−6x+105.7
for x=4
Observed value=80
Predicted value=-6*4+105.7-----> 81.7
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE
so
RESIDUAL VALUE=[80-81.7]----> -1.7-----> -2
point (4,-2)
point 4)
(6, 71)
yˆ=−6x+105.7
for x=6
Observed value=71
Predicted value=-6*6+105.7-----> 69.7
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE
so
RESIDUAL VALUE=[71-69.7]----> 1.3 -----> 1
point (6,1)
point 5)
(7, 63)
yˆ=−6x+105.7
for x=7
Observed value=63
Predicted value=-6*7+105.7-----> 63.7
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE
so
RESIDUAL VALUE=[63-63.7]----> 0.7 -----> 1
point (7,1)
using a graph tool
graph the residual plot for the data set.
the points are
(2,1) (3,1) (4,-2) (6,1) (7,1)
see the attached figure
