Answer:
the observed value of 9 is 13 units lower than the predicted value of 22.
Explanation:
A residual is the difference between the observed value of a data point and the predicted value of that data point based on a given model. In a regression analysis, the residual is calculated using the formula e = y - y', where y is the observed value, y' is the predicted value, and e is the residual.
In this case, we are given the point (4,9) and the regression equation y = 5x + 2. Plugging in the value x = 4 into the regression equation, we get:
y' = 5(4) + 2 = 22
Since we are also given that the observed value of the point (4,9) is 9, we can plug these values into the formula for the residual to calculate the residual:
e = 9 - 22 = -13
Therefore, the residual e when x = 4 is -13. This means that the observed value of 9 is 13 units lower than the predicted value of 22.