问题


There is a single choice question about econometrics. Answer the question by replying A, B, C or D.
Question: The residual from a standard regression model is defined as
A. The difference between the actual value, y, and the mean, y-bar
B. The difference between the fitted value, y-hat, and the mean, y-bar
C. The difference between the actual value, y, and the fitted value, y-hat
D. The square of the difference between the fitted value, y-hat, and the mean, y-bar
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

C. The difference between the actual value, y, and the fitted value, y-hat		 C
deepseekr1

Answer: C

The residual in a standard regression model is defined as the difference between the actual observed value of the dependent variable (\(y\)) and the value predicted by the model (\(\hat{y}\)). This corresponds to **Option C**. The other options describe different concepts:
- **Option A** refers to deviations from the mean (used in total variation).
- **Option B** and **Option D** relate to explained variation (differences between fitted values and the mean or their squares).
Thus, the correct definition of the residual is **C**.		 C
gpto1 C C
GPT-4o C. The difference between the actual value, y, and the fitted value, y-hat C
llama3.1-70B-Instruct

C		 C
llama3.1-405B-Instruct

C. The difference between the actual value, y, and the fitted value, y-hat		 C
DeepSeek-Coder-V2 C C
Qwen2-72B-Instruct C C
baichuan4 C C
doubao C C
minimax C. The difference between the actual value, y, and the fitted value, y-hat C
kimi C. The difference between the actual value, y, and the fitted value, y-hat C
wenxinyiyan C C
zhipu C. The difference between the actual value, y, and the fitted value, y-hat

In econometrics, the residual is the difference between the observed value of the dependent variable (y) and the value predicted by the regression model (y-hat). This is used to measure the error in the model's predictions.		 C
gpto1 C C