金声玉亮2.0模型评测报告

问题

There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: When the point (15,2) is included, the slope of regression line (y= a+ bx) is b= -0.54. The correlation is r= -0.82. When the point is removed, the new slope is -1.04 and the new correlation coefficient is -0.95. What name is given to a point whose removal has this kind of effect on statistical calculations?
A. Outlier
B. Statistically significant point
C. Point of discontinuity
D. Influential point
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	D. Influential point Explanation: An influential point is a data point that has a significant impact on the statistical calculations, such as the slope of the regression line and the correlation coefficient. In this case, the removal of the point (15,2) significantly changes the slope and correlation coefficient, indicating that it is an influential point. An outlier is a data point that is far away from the rest of the data, but it may not necessarily have a significant impact on the statistical calculations. A statistically significant point is a point that is unlikely to occur by chance, but it is not necessarily an influential point. A point of discontinuity is a point where the function is not continuous, but it is not relevant to this context.	D
deepseekr1	The point in question significantly alters the regression slope and correlation coefficient when removed, indicating a strong influence on the statistical model. While outliers may deviate from the data pattern, the critical factor here is the point's impact on the regression parameters. Such a point is termed an influential point because its removal leads to substantial changes in the model's results. Answer: D	D
gpto1	D	D
GPT-4o	D. Influential point	D
llama3.1-70B-Instruct	D	D
llama3.1-405B-Instruct	D. Influential point Explanation: An influential point is a data point that has a significant impact on the statistical calculations, such as the slope of the regression line and the correlation coefficient. In this case, the removal of the point (15,2) significantly changes the slope and correlation coefficient, indicating that it is an influential point. An outlier is a data point that is far away from the rest of the data, but it may not necessarily have a significant impact on the statistical calculations. A statistically significant point is a point that is unlikely to occur by chance, but it is not directly related to the impact on statistical calculations. A point of discontinuity is a point where the function is not continuous, which is not relevant to this scenario.	D
DeepSeek-Coder-V2	D. Influential point	D
Qwen2-72B-Instruct	D. Influential point	D
baichuan4	D. Influential point	D
doubao	D. Influential point. An influential point is one whose removal causes a relatively large change in the values of statistical measures such as the slope and correlation coefficient.	D
minimax	D. Influential point	D
kimi	D. Influential point	D
wenxinyiyan	D Explanation: An "influential point" is one that, when removed from a data set, has a significant effect on the results of statistical calculations such as the slope of a regression line or the correlation coefficient. In this case, the removal of the point (15,2) caused a notable change in both the slope and the correlation coefficient, indicating that it was an influential point. Option A, "outlier", refers to a point that lies outside the general range of other data points, but not all outliers are influential in terms of changing statistical results. Option B, "statistically significant point", is not a standard term used to describe a point that strongly affects statistical calculations. Statistical significance usually refers to the likelihood that an observed effect is real, rather than being due to chance. Option C, "point of discontinuity", is a mathematical term that refers to a point where a function is not continuous. This is not relevant to the context of statistical calculations and the effect of removing a data point.	D
zhipu	D. Influential point An influential point is one that, when removed, significantly changes the results of statistical calculations, such as the slope of the regression line or the correlation coefficient. In this case, removing the point (15,2) drastically changes both the slope and the correlation coefficient, indicating that it is an influential point.	D
gpto1	D	D
deepseekv3	D. Influential point An influential point is a data point whose removal significantly changes the slope of the regression line or other statistical calculations, such as the correlation coefficient. In this case, the slope and correlation coefficient both change substantially when the point (15,2) is removed, indicating that it is an influential point.	D

模型

模型答案

正确答案

金声玉亮2.0

D. Influential point

Explanation: An influential point is a data point that has a significant impact on the statistical calculations, such as the slope of the regression line and the correlation coefficient. In this case, the removal of the point (15,2) significantly changes the slope and correlation coefficient, indicating that it is an influential point. An outlier is a data point that is far away from the rest of the data, but it may not necessarily have a significant impact on the statistical calculations. A statistically significant point is a point that is unlikely to occur by chance, but it is not necessarily an influential point. A point of discontinuity is a point where the function is not continuous, but it is not relevant to this context.

deepseekr1

The point in question significantly alters the regression slope and correlation coefficient when removed, indicating a strong influence on the statistical model. While outliers may deviate from the data pattern, the critical factor here is the point's impact on the regression parameters. Such a point is termed an **influential point** because its removal leads to substantial changes in the model's results.

Answer: **D**

gpto1

GPT-4o

D. Influential point

llama3.1-70B-Instruct

llama3.1-405B-Instruct

D. Influential point

Explanation: An influential point is a data point that has a significant impact on the statistical calculations, such as the slope of the regression line and the correlation coefficient. In this case, the removal of the point (15,2) significantly changes the slope and correlation coefficient, indicating that it is an influential point. An outlier is a data point that is far away from the rest of the data, but it may not necessarily have a significant impact on the statistical calculations. A statistically significant point is a point that is unlikely to occur by chance, but it is not directly related to the impact on statistical calculations. A point of discontinuity is a point where the function is not continuous, which is not relevant to this scenario.

DeepSeek-Coder-V2

D. Influential point

Qwen2-72B-Instruct

D. Influential point

baichuan4

D. Influential point

doubao

D. Influential point. An influential point is one whose removal causes a relatively large change in the values of statistical measures such as the slope and correlation coefficient.

minimax

D. Influential point

kimi

D. Influential point

wenxinyiyan

D

Explanation:
An "influential point" is one that, when removed from a data set, has a significant effect on the results of statistical calculations such as the slope of a regression line or the correlation coefficient. In this case, the removal of the point (15,2) caused a notable change in both the slope and the correlation coefficient, indicating that it was an influential point.

Option A, "outlier", refers to a point that lies outside the general range of other data points, but not all outliers are influential in terms of changing statistical results.

Option B, "statistically significant point", is not a standard term used to describe a point that strongly affects statistical calculations. Statistical significance usually refers to the likelihood that an observed effect is real, rather than being due to chance.

Option C, "point of discontinuity", is a mathematical term that refers to a point where a function is not continuous. This is not relevant to the context of statistical calculations and the effect of removing a data point.

zhipu

D. Influential point

An influential point is one that, when removed, significantly changes the results of statistical calculations, such as the slope of the regression line or the correlation coefficient. In this case, removing the point (15,2) drastically changes both the slope and the correlation coefficient, indicating that it is an influential point.

gpto1

deepseekv3

D. Influential point

An influential point is a data point whose removal significantly changes the slope of the regression line or other statistical calculations, such as the correlation coefficient. In this case, the slope and correlation coefficient both change substantially when the point (15,2) is removed, indicating that it is an influential point.