Ask a New Question
Menu

Use the tables to create scatterplots and determine which scatterplot shows a linear association.(1 point) Responses x 5 8 2 4 6 12 10 1 3 7 y 800 700 350 450 500 1000 900 250 400 750 x 5 8 2 4 6 12 10 1 3 7 y 800 700 350 450 500 1000 900 250 400 750 x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 300 700 1000 650 300 100 700 x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 300 700 1000 650 300 100 700 x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 500 500 400 650 150 400 750 x 5 8 2 4 6 12 10 1 3 7 y 550 800 250 500 500 400 650 150 400 750 x 5 8 2 4 6 12 10 1 3 7 y 550 800 350 450 700 1000 900 250 400 750

1 answer

To determine which scatterplot shows a linear association based on the provided data sets, we need to assess the relationship between the x and y values in each table. A linear association would indicate that as x increases, y increases or decreases consistently without a lot of variability.

The datasets provided are as follows:

Data Set 1:

  • x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
  • y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750

Data Set 2:

  • x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
  • y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700

Data Set 3:

  • x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
  • y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750

Data Set 4:

  • x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
  • y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750

Data Set 5:

  • x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
  • y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750

Analysis

  1. Data Set 1: The y values fluctuate quite a bit, especially around the middle range, meaning that there is no clear linear trend.

  2. Data Set 2: The y values also vary significantly without a consistent upward or downward trend, indicating a lack of linear association.

  3. Data Set 3: The y values show a mix of highs and lows, but there is a notable lack of consistency that suggests a non-linear association.

  4. Data Set 4: Similar to Data Set 3, the y values fluctuate without showing any clear trend.

  5. Data Set 5: The values fluctuate, but there appears to be a moderate trend towards a linear relationship, especially in the higher x values where y tends to be higher.

Conclusion

From the assessments above, none of the provided datasets show a very strong linear association. However, Data Set 5 has a slight upward trend, whereas the other data sets exhibited more significant fluctuations without any discernible pattern. Therefore, Data Set 5 would be the one that potentially shows the closest linear association.

For the most accurate results, creating scatterplots for each dataset would visually demonstrate these relationships, but based on analysis, Data Set 5 shows the most potential for a linear relationship.