Question
Use the tables to create scatterplots and determine which scatterplot shows a non-linear association.
x 50 46 98 59 78 64 68 53 70 72
y 75 71 90 55 70 100 90 25 40 76
x 50 46 98 59 78 64 68 53 70 72 y 75 71 90 55 70 100 90 25 40 76
x 50 46 90 59 78 64 68 53 70 72
y 75 71 100 80 90 82 85 77 87 89
x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89
x 50 46 80 59 78 64 68 53 70 68
y 90 100 57 80 60 75 72 82 70 67
x 50 46 80 59 78 64 68 53 70 68 y 90 100 57 80 60 75 72 82 70 67
x 50 46 80 59 78 64 68 53 70 68
y 35 30 75 45 70 50 55 36 62 67
x 50 46 98 59 78 64 68 53 70 72
y 75 71 90 55 70 100 90 25 40 76
x 50 46 98 59 78 64 68 53 70 72 y 75 71 90 55 70 100 90 25 40 76
x 50 46 90 59 78 64 68 53 70 72
y 75 71 100 80 90 82 85 77 87 89
x 50 46 90 59 78 64 68 53 70 72 y 75 71 100 80 90 82 85 77 87 89
x 50 46 80 59 78 64 68 53 70 68
y 90 100 57 80 60 75 72 82 70 67
x 50 46 80 59 78 64 68 53 70 68 y 90 100 57 80 60 75 72 82 70 67
x 50 46 80 59 78 64 68 53 70 68
y 35 30 75 45 70 50 55 36 62 67
Answers
GPT-4o mini
To identify which scatterplot demonstrates a non-linear association, we'll analyze the provided sets of x and y values and look for recognizable patterns in the relationships between the two variables.
### Dataset 1:
**x:** 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
**y:** 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
- **Scatterplot:** In this scatterplot, the points do not follow a clear linear trend. Instead, the values seem scattered, and the relationship may be more complex.
### Dataset 2:
**x:** 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
**y:** 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
- **Scatterplot:** This set has points that increase more consistently. It suggests a positive linear association as the values of y increase as x increases.
### Dataset 3:
**x:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
**y:** 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
- **Scatterplot:** Particularly in the first half, this dataset shows an initial increase but then flattens out and declines with some values. This indicates a slight non-linear relationship.
### Dataset 4:
**x:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
**y:** 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
- **Scatterplot:** The points in this dataset appear more scattered and do not suggest a clear upward or downward trend. There is no visible linear relationship.
### Summary:
Based on the analysis of the datasets, the first dataset and the third dataset exhibit non-linear associations due to their scattered points lacking a consistent linear trend. However, if we are looking for the one that has a more distinct non-linearity, **Dataset 1** likely shows the most pronounced non-linear association.
To summarize the results:
- **Dataset 1:** Non-linear association
- **Dataset 2:** Strong linear association
- **Dataset 3:** Non-linear association
- **Dataset 4:** Lack of clear association
Therefore, **scatterplots for Dataset 1 and Dataset 3** can be classified as non-linear, with Dataset 1 being the most evident when identifying a clear non-linear relationship.
### Dataset 1:
**x:** 50, 46, 98, 59, 78, 64, 68, 53, 70, 72
**y:** 75, 71, 90, 55, 70, 100, 90, 25, 40, 76
- **Scatterplot:** In this scatterplot, the points do not follow a clear linear trend. Instead, the values seem scattered, and the relationship may be more complex.
### Dataset 2:
**x:** 50, 46, 90, 59, 78, 64, 68, 53, 70, 72
**y:** 75, 71, 100, 80, 90, 82, 85, 77, 87, 89
- **Scatterplot:** This set has points that increase more consistently. It suggests a positive linear association as the values of y increase as x increases.
### Dataset 3:
**x:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
**y:** 90, 100, 57, 80, 60, 75, 72, 82, 70, 67
- **Scatterplot:** Particularly in the first half, this dataset shows an initial increase but then flattens out and declines with some values. This indicates a slight non-linear relationship.
### Dataset 4:
**x:** 50, 46, 80, 59, 78, 64, 68, 53, 70, 68
**y:** 35, 30, 75, 45, 70, 50, 55, 36, 62, 67
- **Scatterplot:** The points in this dataset appear more scattered and do not suggest a clear upward or downward trend. There is no visible linear relationship.
### Summary:
Based on the analysis of the datasets, the first dataset and the third dataset exhibit non-linear associations due to their scattered points lacking a consistent linear trend. However, if we are looking for the one that has a more distinct non-linearity, **Dataset 1** likely shows the most pronounced non-linear association.
To summarize the results:
- **Dataset 1:** Non-linear association
- **Dataset 2:** Strong linear association
- **Dataset 3:** Non-linear association
- **Dataset 4:** Lack of clear association
Therefore, **scatterplots for Dataset 1 and Dataset 3** can be classified as non-linear, with Dataset 1 being the most evident when identifying a clear non-linear relationship.