Jazmin can conclude the following about the appropriateness of the linear model based on the trend line equation and the correlation coefficient:
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Negative Slope: The trend line equation \( y = -0.694x + 17.22 \) indicates that there is a negative linear relationship between the variables \( x \) and \( y \). As \( x \) increases, \( y \) tends to decrease.
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Correlation Coefficient: The correlation coefficient \( r = -0.9153 \) is a strong negative correlation. The value of \( r \) ranges from -1 to 1, where values close to -1 indicate a strong negative linear relationship, values close to 0 indicate no linear relationship, and values close to 1 indicate a strong positive linear relationship. Since -0.9153 is closer to -1, it suggests that the linear model is a very good fit for the data.
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Linearity: The strong correlation suggests that a linear model is appropriate for the dataset. The relationship is not only strong but also consistent, as indicated by the negative coefficient.
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Conclusion: Based on this information, Jazmin should conclude that the linear model she found is appropriate for the dataset, as the negative trend and strong correlation coefficient indicate a reliable linear relationship that could be used for predictions or further analysis.
Overall, Jazmin can confidently use the linear model for interpreting her data due to the strong negative correlation and the presence of a clear linear trend.