Question

These are the values in Ariel’s data set. (1, 67), (3, 88), (5,97), (6, 101), (8, 115) Ariel determines the equation of a linear regression line to be yˆ=6.5x+63.8 . Use the point tool to graph the residual plot for the data set. Round residuals to the nearest unit as needed.

Answer 1

Answer:

The residual points are (1,-3.3)(3,4.7)(5,0.7)(6,-1.8)(8,-0.8).

Step-by-step explanation:

Given : These are the values in Ariel’s data set. (1, 67), (3, 88), (5,97), (6, 101), (8, 115) Ariel determines the equation of a linear regression line to be y=6.5x+63.8 .

To find : Use the point tool to graph the residual plot for the data set. Round residuals to the nearest unit as needed.

Solution :

A residual is defined as the difference between the predicted value and the actual value.

We have given a linear regression line which gives you predicted output.

Actual output are given in a point.

So, Taking one by one to find the residual value.

1) (1,67)

Actual = 67          

Predicted = y=6.5(1)+63.8=70.3  

Residual = 67-70.3=-3.3

The residual at x = 1 is -3.3.

2) (3,88)

Actual = 88

Predicted = y=6.5(3)+63.8=83.3

Residual = 88-83.3=4.7

The residual at x = 3 is 4.7.

3) (5,97)

Actual = 97

Predicted = y=6.5(5)+63.8=96.3

Residual = 97-96.3=0.7

The residual at x = 5 is 0.7.

4) (6,101)

Actual = 101

Predicted = y=6.5(6)+63.8=102.8

Residual = 101-102.8=-1.8

The residual at x = 6 is -1.8.

5) (8,115)

Actual = 115

Predicted = y=6.5(8)+63.8=115.8

Residual = 115-115.8=-0.8

The residual at x = 8 is -0.8.

Therefore, The residual points are (1,-3.3)(3,4.7)(5,0.7)(6,-1.8)(8,-0.8).

Answer 2

(3,5)
(1,-3)
(5,1)
(6,-2)
(8,-1)