Given:
The regression equation for change in temperature, y, to amount of rain, r, is given by
[tex]\hat{y}=0.2-1.4r[/tex]
The observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.
To find:
The residual and interpret it.
Solution:
According to the question, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees.
So, the actual value is 2.3 degrees.
Put r=0.4 in the given equation, to find the predicted value.
[tex]\hat{y}=0.2-1.4(0.4)[/tex]
[tex]\hat{y}=0.2-0.56[/tex]
[tex]\hat{y}=-0.36[/tex]
We know that,
Residual = Actual value - Predicted value
[tex]Residual=2.3-(-0.36)[/tex]
[tex]Residual=2.3+0.36[/tex]
[tex]Residual=2.66[/tex]
Residual is positive because predicated value is less than the actual value.
So, the regression line underpredicts the temperature change.
Therefore, the correct option is B.
