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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's findings provide important insights into the appropriateness of the linear model she found for her dataset.

  1. Trend Line Equation: The equation of the trend line is \( y = -0.694x + 17.22 \). This indicates a negative linear relationship between the variables. As \( x \) increases, \( y \) tends to decrease.

  2. Correlation Coefficient: The correlation coefficient (denoted as \( r \)) is -0.9153. This value is quite high in absolute terms, meaning that there is a strong negative linear relationship between the two variables. The correlation coefficient can range from -1 to 1, where a value close to -1 indicates a strong negative correlation, 0 indicates no correlation, and a value close to 1 indicates a strong positive correlation.

Given the strong negative correlation coefficient of -0.9153, Jazmin can conclude that a linear model is indeed appropriate for her dataset. This high negative correlation suggests that the linear model captures the relationship between the two variables well.

Conclusion:

Jazmin should conclude that the linear model is appropriate for her dataset since the correlation coefficient indicates a strong negative linear relationship between the variables.