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Which associations best describe the scatter plot?

Select each correct answer.

Responses

Negative association
Negative association

Positive association
Positive association

Nonlinear association
Nonlinear association

Linear association
Linear association
Scatter plot on a first quadrant coordinate grid. The horizontal axis is labeled Time, in minutes. The vertical axis is labeled Distance, in feet. Points are plotted at (one, fifteen), (two, eleven), (three, eight), (four, six), (five, five), (six, four), (seven, three), (eight, three), (nine, three), (ten, three).

1 answer

To analyze the scatter plot based on the provided points, we can evaluate the relationships between the points plotted as follows:

  1. Negative association: A negative association means that as the independent variable (Time) increases, the dependent variable (Distance) decreases. Looking at the data points, we can see that as time increases, the distance tends to decrease (from 15 feet at 1 minute down to 3 feet by 9 and 10 minutes). Therefore, this association holds true.

  2. Positive association: A positive association means that as one variable increases, the other variable also increases. Based on the data provided, this is not the case since increasing time results in decreasing distance. Thus, this does not apply.

  3. Nonlinear association: A nonlinear association indicates that the relationship between the variables does not follow a straight line. In this case, while the distance decreases with time, the rate of change is not consistent. For example, the distance falls rapidly at first but then levels out (3 feet from minute 8 to minute 10). Hence, this can be considered as having a nonlinear association.

  4. Linear association: A linear association means that the data points can be approximated by a straight line. Since the relationship between time and distance appears to be decreasing but not in a straight line across all points, this does not apply.

Based on this analysis, the correct associations that best describe the scatter plot are:

  • Negative association
  • Nonlinear association