In the equation c = + i + u,c denotes consumption and i denotes income.What is the residual for the 5^th observation if =$500 and =$475?

Question

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The residual is the difference between the predicted consumption and the actual consumption: Residual = c(predicted) - c(actual) To predict consumption, we use the equation given: c = 11eab0c9_90f3_2413_8f52_45e1591f3137_TB2132_11 + 11eab0c9_90f3_4b24_8f52_25365b6e5532_TB2132_11 i Plugging in the values given, we get: c = 11(500) + 11(475)i c = 5500 + 5225i So the predicted consumption for the 5^th observation is $5500 + $5225i. But we are not given the actual consumption, so we cannot calculate the exact residual. However, we know that the imaginary part of the predicted consumption depends on income, so it will not change based on the values given for 11eab0c9_90f3_4b25_8f52_a1319fcd5eef_TB2132_11 and 11eab0c9_90f3_7236_8f52_57376facb2db_TB2132_11. Therefore, the residual will only depend on the real part of the predicted consumption: Residual = $5500 - actual consumption Since we don't know the actual consumption, we can't calculate the exact residual, but we can tell that it will be some multiple of $25 (the difference between the values given for 11eab0c9_90f3_4b25_8f52_a1319fcd5eef_TB2132_11 and 11eab0c9_90f3_7236_8f52_57376facb2db_TB2132_11). The only answer choice that is a multiple of $25 is C.

In the Equation C = + I