To analyze the statements regarding the relationship between Beth's son's age and weight using a scatter plot, you'll first need to create the scatter plot in a graphing calculator like DESMOS. Here’s how you can go about it:
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Input Data: Enter the data from the table into DESMOS. You would typically have two columns, one for age (x-axis) and one for weight (y-axis).
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Create Scatter Plot: Use the plotted points to visualize the relationship between age and weight. This will help you determine any trends.
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Line of Best Fit: To evaluate the provided linear equation \(y = 5x + 15\), you can plot this line on the same graph and see how well it fits the data points.
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Evaluate Correlation: Look at the scatter plot's overall shape. If the points seem to follow an upward or downward trend, then there is a correlation; if they are randomly scattered, there is likely no correlation.
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Check Statements:
- Statement 1: "The data can be represented with a line of best fit \(y = 5x + 15\)" - Use the scatter plot and compare how well the line fits the data points. If the points closely follow this line, it's true; if not, it's false.
- Statement 2: "There is no correlation between the recorded age and weight." - Observe the scatter plot; if you see a trend, it would be false, but no clear trend suggests it could be true.
- Statement 3: "The data suggests a linear association between the recorded age and weight." - Again, based on your observation of the scatter plot, a clear upward or downward trend suggests a linear association (true), while scattered points indicate no association (false).
After you have conducted the analysis, you should be able to determine which statements are true or false based on the visual representation and trends observed in the scatter plot.