Suppose that for x = 3, the predicted value is y = 7. The data pair (3, 10) is part of the sample data. What is the value of the residual for x = 3?
Oh, I see we have a "value of the residual" question here. Well, the residual is like that one friend who keeps showing up uninvited to a party. You didn't really expect them to be there, but they just won't leave. In this case, the residual is the difference between the actual observed value and the predicted value. So, for x = 3, the predicted value is y = 7, but the actual value is y = 10. Therefore, the residual is just the difference between the two, which is 10 - 7 = 3. So, the value of the residual for x = 3 is 3. It's like that friend who always brings their own drama to the party!
To find the residual for a given data point, we need to subtract the predicted value from the actual value. In this case, the predicted value for x=3 is y=7. However, we also have the data pair (3, 10), which means that when x=3, the actual value is y=10.
The residual for x=3 can be found by subtracting the predicted value from the actual value:
Residual = Actual value - Predicted value
= 10 - 7
= 3
Therefore, the value of the residual for x=3 is 3.