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Jazmin used a graphing calculator to graph a given dataset. She found that the trend line of her data is

y=-0.694x+17.22 and that the correlation coefficient is −0.9153. What conclusion should Jazmin make about the appropriateness of the linear model she found?

1 answer

Jazmin should conclude that the linear model she found is appropriate for her dataset. Here are the key points to support this conclusion:

  1. Correlation Coefficient: The correlation coefficient (r) is -0.9153, which is close to -1. This indicates a strong negative linear relationship between the variables. A strong correlation suggests that a linear model is suitable for describing the relationship in the data.

  2. Slope of the Trend Line: The slope of the trend line is -0.694, which further confirms the negative relationship between the variables. Since the slope is not close to zero, it suggests that changes in the independent variable (x) have a significant effect on the dependent variable (y).

  3. Visual Inspection: Although it's not stated explicitly, if Jazmin visually inspected her graph and saw that the points are close to the trend line, it would further support the validity of the linear model.

In conclusion, given the strong negative correlation and the linear trend line, Jazmin’s linear model appears to be a good fit for her dataset, indicating that it appropriately represents the relationship between the variables involved.