Jazmin's findings indicate a strong negative correlation between the variables represented by the dataset. The trend line equation is \( y = -0.694x + 17.22 \), where the slope of -0.694 suggests that as \( x \) increases, \( y \) decreases. Additionally, the correlation coefficient \( r = -0.9153 \) is very close to -1, which signifies a very strong negative linear relationship.
Given these points, Jazmin can conclude the following about the appropriateness of the linear model:
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Strength of Correlation: The correlation coefficient of -0.9153 indicates a strong linear relationship between the variables. A value close to -1 means that the linear model is likely a good fit for the data.
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Direction of Relationship: The negative value of the correlation coefficient confirms that there is an inverse relationship between the variables.
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Linearity: Since the correlation coefficient is strong, it suggests that a linear model is appropriate for this dataset. However, it is important to ensure that the data does not exhibit non-linear patterns, as that could affect the validity of the linear model.
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Predictive Power: The strength of the correlation implies that the linear equation can be used to make useful predictions about \( y \) based on values of \( x \).
Overall, based on the strong negative correlation and the linear trend seen in her data, Jazmin can confidently conclude that the linear model she found is appropriate for describing the relationship in her dataset. However, it would be prudent for her to visually examine the scatter plot of the data to confirm that it appears linear and to check for any outliers or patterns that could influence the model.