Question

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
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
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
550 800 350 450 700 1000 900 250 400 750

1 answer

To determine which scatterplot shows a linear association, we can describe how each dataset would be plotted and which may indicate a linear relationship between the x and y values.

  1. First dataset:

    • x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
    • y values: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700
    • Analysis: These points vary considerably with no clear linear trend.
  2. Second dataset:

    • x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
    • y values: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750
    • Analysis: These points also show some variation, but they don’t align in a straight line.
  3. Third dataset:

    • x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
    • y values: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750
    • Analysis: The y values vary considerably with respect to the x values, showing no clear linear pattern.
  4. Fourth dataset:

    • x values: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7
    • y values: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750
    • Analysis: Similar to the others, this dataset also fluctuates without showing a strong linear relationship.

It appears that none of the datasets clearly establish a linear association upon quick analysis. However, visually plotting the scatterplots for each dataset will give a clearer indication of which dataset may have a better linear fit.

Conclusion:

After considering the patterns, if you had to choose, the dataset that typically has the highest variance in both x and y being unevenly spaced could potentially suggest less linearity. If you have the means to plot these datasets, that would provide the most definitive answer.

If you want, further analysis can be done with specific calculations, like correlation coefficients or regression analysis, to quantify their linear correlations. If you need assistance on computational methods, feel free to ask!