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 . use the point tool to graph the residual plot for the data set. round residuals to the nearest unit as needed.

The residual points are (1,6.2)(2,-3.9)(3,-2)(4,-9.1)(5,8.8).

Refer the attached figure.

Step-by-step 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.

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