Answer:
The residual points are (1,6.2)(2,-3.9)(3,-2)(4,-9.1)(5,8.8).
Refer the attached figure.
Explanation:
Given : These are the values in Simcha’s data set (1, 18), (2, 22), (3, 38), (4, 45), (5, 77) . Simcha determines the equation of a linear regression line to be yˆ=14.1x−2.3 .
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 i.e. Residual=Actual - Predicted
We have given a linear regression line which gives you predicted output i.e. yˆ=14.1x−2.3
Now, we find the residual value.
1) (1,18)
Actual = 18
Predicted = y=14.1(1)-2.3=11.8
Residual = 18-11.8 =6.2
The residual at x = 1 is 6.2.
2) (2,22)
Actual = 22
Predicted = y=14.1(2)-2.3=25.9
Residual = 22-25.9=-3.9
The residual at x = 2 is -3.9
3) (3,38)
Actual = 38
Predicted = y=14.1(3)-2.3=40
Residual = 38-40=-2
The residual at x = 3 is -2.
4) (4,45)
Actual = 45
Predicted = y=14.1(4)-2.3=54.1
Residual = 45-54.1=-9.1
The residual at x = 4 is -9.1.
5) (5,77)
Actual = 77
Predicted = y=14.1(5)-2.3=68.2
Residual = 77-68.2=8.8
The residual at x =5 is 8.8
Therefore, The residual points are (1,6.2)(2,-3.9)(3,-2)(4,-9.1)(5,8.8).
Refer the attached figure below showing the residual points.
The data points shown in red color.
The residual points shown in blue color.