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Data Set A: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)

Data Set B: (3,4), (4,6), (5,8), (6,10), (7,12)

Data Set C: (0,1), (3,3), (6,9), (9,27), (12,81)

Data Set D: (2,4), (−1,2), (7,16), (−4,32), (1,64)

Create a scatterplot for each of the data sets shown. Which data set can reasonably be modeled by a linear relationship?

Responses

Data Set B

Data Set A

Data Set C

Data Set D

1 answer

To determine which data set can reasonably be modeled by a linear relationship, we need to consider the nature of the relationships represented in each dataset.

  1. Data Set A:

    • The points are: (0, 2), (1, 4), (2, 8), (3, 16), (4, 32), (5, 64).
    • The y-values increase exponentially as the x-values increase. Therefore, this data set cannot be modeled linearly.

  2. Data Set B:

    • The points are: (3, 4), (4, 6), (5, 8), (6, 10), (7, 12).
    • The y-values increase consistently by 2 as the x-values increase by 1. This data set forms a straight line and can be modeled linearly.

  3. Data Set C:

    • The points are: (0, 1), (3, 3), (6, 9), (9, 27), (12, 81).
    • The y-values suggest an exponential growth pattern once the points exceed (6, 9), so a linear model is not appropriate.

  4. Data Set D:

    • The points are: (2, 4), (−1, 2), (7, 16), (−4, 32), (1, 64).
    • The relationship appears to be non-linear based on the disparate increases in y-values as the x-values change. Hence, this data set does not represent a linear relationship.

Based on this analysis, the data set that can reasonably be modeled by a linear relationship is:

Data Set B.