Question

The linear regression equation shown at the right is y = 4.7x + 51. The scatter plot at x = 5 is (5,90). What is the residual associated with the point where x = 5?

A. 7.3
B. 6.7
C. 4.7
D. 0.7

Answer 1

The residual associated with the point where x = 5 is 20.5. None of the given options is answer.

Step-by-step explanation:

Predicted value: The linear regression equation predicts a value of y = 4.7(5) + 51 = 69.5 for x = 5.

Actual value: The scatter plot shows the actual value of y for x = 5 as 90.

Residual calculation: The residual is the difference between the actual and predicted values: 90 - 69.5 = 20.5.

The linear regression equation predicts a value of 69.5 for y when x is 5, but the actual value from the scatter plot is 90. The resulting residual, calculated as the difference between the actual and predicted values, is 20.5. This positive residual suggests that the model underestimates the y value at x = 5, highlighting a potential limitation in the accuracy of the linear regression prediction for this specific data point.

None of the given options is answer.