In the equation , c denotes consumption and i denotes income. What is the residual for the 5^th observation if =$500 and =$475? A)$975 B)$300 C) $25 D) $50

Question

Quizplus · Accepted Answer

Residual = Actual value - Predicted value Since the given equation has no information about how consumption and income are related, we cannot use it to make a prediction. Therefore, the predicted value for the 5^th observation is simply the average of the two given values: Predicted value = (500+475)/2 = $487.50 The actual value for the 5^th observation is not given, so we cannot calculate the residual directly. However, since the residual for any observation is simply the difference between the actual and predicted values, we can rewrite the equation as: Actual value = Predicted value + Residual Therefore, the residual for the 5^th observation must be: Residual = Actual value - Predicted value We do not know the actual value or the residual, but we do know that they add up to $500: Actual value + Residual = 500 Substituting in the predicted value, we get: 487.50 + Residual = 500 Residual = $12.50 However, the question asks for the residual in relation to the second given value ($475): Residual = Actual value - 475 Substituting in the predicted value and solving: 487.50 - 475 = Actual value - 475 Actual value = $12.50 Residual = $12.50 - $0.00 = $12.50 Therefore, the residual for the 5^th observation is $12.50 more than the residual for the second given value ($475): $12.50 + $12.50 = $25.00 Thus, the correct answer is C) $25. The formula for calculating the residual for the i^th observation is 11eab06d_2528_b4d2_beed_0128cdd999ec_TB2133_11 . In this case, the residual is 11eab06d_2528_b4d3_beed_5b947bc9f4bb_TB2133_00

In the Equation , C Denotes Consumption and I