Question

These are the values in Devante’s data set. (2, 94.5), (3, 89), (4,80), (6, 71), (7, 63) Devante determines the equation of a linear regression line to be yˆ=−6x+105.7 .
Use the point tool to graph the residual plot for the data set.

Round residuals to the nearest unit as needed.

Answer 1

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