To determine which table has a non-linear association, we would typically graph the points on a scatterplot and visually inspect for patterns.
Here are the coordinates for each of the tables you provided:
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Table A:
x: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100 y: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 -
Table B:
x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 y: 60, 75, 80, 95, 65, 50, 70, 82, 78, 100 -
Table C:
x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 y: 60, 75, 90, 97, 65, 50, 70, 60, 78, 100 -
Table D:
x: 2, 5, 7, 9, 3, 1, 4, 8, 6, 10 y: 60, 75, 80, 65, 22, 59, 86, 100, 25, 97
Analysis of Data:
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Table A:
- As \( x \) increases, \( y \) generally increases. This suggests a potential linear relationship.
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Table B:
- Here, as \( y \) values increase, the corresponding \( x \) values also trend upwards, which suggests a linear relationship as well.
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Table C:
- The pattern is more scattered, and there are some values where \( y \) decreases significantly despite \( x \) increasing. This indicates a possible non-linear association.
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Table D:
- The relationship looks more random with significant decreases in \( y \) as \( x \) increases. This also indicates a potential non-linear association.
Conclusion: To ascertain which table has a non-linear association, Table C and Table D show more irregular patterns, but Table D appears to be particularly non-linear due to its larger variability and lack of straightforward increasing or decreasing trend.
Thus, Table D is the one that has a clear non-linear association based on the data provided.
For a more definitive answer, you would want to plot these points on a scatterplot, but from the analysis above, you can conclude that Table D seems to be the best candidate for a non-linear relationship.
3 answers