Answer:
Complete step by step explanation along with graphs are provided below.
Step-by-step explanation:
We are given a linear regression model described by the equation,
Where x is the age in years of the Geometrees and f(x) is the corresponding height of the Geometrees.
Residual value:
A residual value shows the position of a data point with respect to the regression line.
The Residual value is calculated by
Residual value = Observed value - Predicted value
Where observed values are already given in the question.
The predicted values are calculated as
For x = 1
F(x) = 1.3(1) + 9.2 = 1.3 + 9.2 = 10.5
For x = 2
F(x) = 1.3(2) + 9.2 = 2.6 + 9.2 = 11.8
For x = 3
F(x) = 1.3(3) + 9.2 = 3.9 + 9.2 = 13.1
For x = 4
F(x) = 1.3(4) + 9.2 = 5.2 + 9.2 = 14.4
The rest of the predicted values are calculated similarly and are given in the attached table.
Now we can find out the residual values,
Residual value = Observed value - Predicted value
Residual value = 9 - 10.5 = -1.5
Residual value = 12 - 11.8 = 0.2
Residual value = 14 - 13.1 = 0.9
Residual value = 15 - 14.4 = 0.6
The rest of the residual values are calculated similarly and are given in the attached table.
A plot of residual values vs age of Geometrees is attached.
A plot of residual values vs height of Geometrees is also attached.
Note:
A residual value closer to 0 is desired since such values means that the regression best fits the data points.
