| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. OLS minimises the sum of the squares of the vertical distances from the points to the line. In Ordinary Least Squares (OLS) estimation, the goal is to find the best-fitting line that minimizes the sum of the squared errors (SSE) between the observed data points and the predicted values. The errors are measured as the vertical distances between the data points and the line. By minimizing the sum of the squares of these vertical distances, OLS finds the line that best fits the data. Therefore, option B is the correct answer. |
B |
| deepseekr1 | The correct answer is **B**. OLS (Ordinary Least Squares) estimation minimizes the sum of the **squares** of the **vertical distances** (residuals) between the observed values of the dependent variable and the values predicted by the regression line. This is a defining characteristic of OLS, distinguishing it from methods that minimize absolute vertical distances (A) or horizontal distances (C, D). Answer: B |
B |
| gpto1 | B | B |
| GPT-4o | B. OLS minimises the sum of the squares of the vertical distances from the points to the line | B |
| llama3.1-70B-Instruct | B |
B |
| llama3.1-405B-Instruct | B. OLS minimises the sum of the squares of the vertical distances from the points to the line. In Ordinary Least Squares (OLS) estimation, the goal is to find the best-fitting line that minimizes the sum of the squared errors (SSE), where the errors are the vertical distances between the observed data points and the predicted values based on the line. This is why OLS is also known as the "least squares" method. The correct answer is B, as OLS minimizes the sum of the squares of the vertical distances from the points to the line. The other options are incorrect: * A is incorrect because OLS does not minimize the sum of the vertical distances, but rather the sum of the squares of those distances. * C is incorrect because OLS does not minimize the sum of the horizontal distances. * D is incorrect because OLS does not minimize the sum of the squares of the horizontal distances. Therefore, the correct answer is B. |
B |
| DeepSeek-Coder-V2 | B | B |
| Qwen2-72B-Instruct | B. OLS minimises the sum of the squares of the vertical distances from the points to the line | B |
| baichuan4 | B | B |
| doubao | B | B |
| minimax | B. OLS minimises the sum of the squares of the vertical distances from the points to the line | B |
| kimi | B. OLS minimises the sum of the squares of the vertical distances from the points to the line | B |
| wenxinyiyan | B Explanation: OLS (Ordinary Least Squares) estimation aims to minimise the sum of the squared vertical distances (also known as residuals or errors) from the observed data points to the estimated regression line. This criterion is known as the "least squares" criterion, and it ensures that the line fitted to the data is the one that minimises the overall prediction error, measured as the sum of squared distances from the data points to the line along the vertical axis. Therefore, option B "OLS minimises the sum of the squares of the vertical distances from the points to the line" is the correct answer. Options A, C, and D are incorrect because they do not accurately describe the minimisation criterion used in OLS estimation. |
B |
| zhipu | B. OLS minimises the sum of the squares of the vertical distances from the points to the line Explanation: Ordinary Least Squares (OLS) estimation is designed to find the line that best fits the data by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line. This method ensures that the total squared error is as small as possible, leading to the most accurate linear approximation of the data. |
B |
| gpto1 | B | B |