Question

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?

Answer 1

Jazmin's findings can be interpreted as follows:

1. **Trend Line Equation**: The trend line of her data, represented by the equation \( y = -0.694x + 17.22 \), indicates a negative linear relationship between the variables \( x \) and \( y \). This means that as \( x \) increases, \( y \) tends to decrease.

2. **Correlation Coefficient**: The correlation coefficient, \( r = -0.9153 \), is quite close to -1. This indicates a strong negative linear relationship between the two variables. In general, correlation coefficients range from -1 to 1, where values closer to -1 suggest a strong negative correlation, values closer to 1 suggest a strong positive correlation, and values near 0 suggest no correlation.

### Conclusion:

Given the strong negative correlation coefficient and the linear trend line, Jazmin can conclude that the linear model is appropriate for the dataset. The fact that the correlation is significantly negative suggests that the linear relationship is both strong and reliable, making the linear model a good fit for predicting \( y \) based on \( x \).

However, she should also consider checking for linearity in the residuals and any potential outliers or patterns that could indicate that a more complex model is needed. But based solely on the correlation coefficient and the trend line equation, a linear model appears to be suitable for her dataset.