In the equation _{Savings=\beta_0+\beta_1Income+\mu}. What is the residual for the 10th observation if \hat{savings}=$400 and savings=$1000?

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BlackTom AI · Accepted Answer

Question restatement: The equation for savings is Savings = β0 + β1 Income + μ, and we’re asked to find the residual for the 10th observation given that the predicted savings hat{Savings} = 400 and the actual savings is 1000.

First, recall the definition of a residual in regression: residual = observed value − predicted value.

Applying this to the 10th observation:
- Observed savings = 1000
- Predicted savings hat{Savings} = 400

Compute the residual: 1000 − 400 = 600.

Now consider the answer option provided: "$600". This matches the calculated residual value exactly.

Why the other potential interpretations would be incorrect (if you consider alternatives):
- If one mistakenly used predicted minus observed, the residual would be 400 − 1000 = −600, which is not the standard residual definition.
- If one confused residual with the forecast error or misread the variables, they might arrive at a different magnitude or sign, but the conventional residual formula is observed minus predicted, yielding +600 in this case.

Summary: The residual for the 10th observation is 600, aligning with the standard residual calculation and the given option "$600".

LA-ECON-3503-811-13824-202520 Quiz 1

In the equation _{Savings=\beta_0+\beta_1Income+\mu}. What is the residual for the 10th observation if \hat{savings}=$400 and savings=$1000?

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