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Beth has been recording her son's weight each year for the past 10 years, as shown in the table below:

Age (years): 1,2,3,4,5,6,7,8,9,10
Weight (pounds): 21, 28,31,35,40,46,51,57,64,71

Using this table, draw a scatter plot on the graphing calculator DESMOS to determine if the statements below are true or false.

(3 points)
True False
The data can be represented with a line of best fit y=5x+15

There is no correlation between the recorded age and weight.

The data suggests a linear association between the recorded age and weight.

1 answer

To assess the statements regarding Beth's son's weight over the years, we can analyze the data as follows:

  1. Scatter Plot: You can input the data into Desmos to create a scatter plot. The points are:

    • (1, 21)
    • (2, 28)
    • (3, 31)
    • (4, 35)
    • (5, 40)
    • (6, 46)
    • (7, 51)
    • (8, 57)
    • (9, 64)
    • (10, 71)

  2. Line of Best Fit: To determine if the line of best fit (y = 5x + 15) adequately represents the data, you can check the fit visually on the scatter plot or calculate the correlation coefficient. For a line of best fit to be accurate, it should closely follow the trend of the data points.

  3. Correlation: The correlation between age and weight appears to be positive, meaning that as age increases, weight also increases. A strong positive correlation indicates a linear relationship.

  4. Analysis of Statements:

    • "The data can be represented with a line of best fit y=5x+15.":

      • False. The slope seems inconsistent with the actual data. You can check this by observing that the weight does not consistently increase by 5 pounds for each additional year. The increase in weight appears to be larger as age increases.

    • "There is no correlation between the recorded age and weight.":

      • False. There is a clear positive correlation based on the observed data, as weight increases with age.

    • "The data suggests a linear association between the recorded age and weight.":

      • True. The scatter plot will show a linear trend, indicating a strong association between age and weight.

In summary:

  • The first statement is False.
  • The second statement is False.
  • The third statement is True.