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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? explain in 8th grade terms

1 answer

Jazmin found a trend line equation and a correlation coefficient for her data. The trend line equation is y = -0.694x + 17.22, and the correlation coefficient is -0.9153.

Here’s what this means:

  1. Trend Line: The trend line equation shows that as the value of x increases, the value of y decreases. This suggests there is a negative relationship between the two variables. In everyday terms, if you were to plot the points of her data on a graph, the trend line would slope downwards.

  2. Correlation Coefficient: The correlation coefficient (the number -0.9153) tells Jazmin how strong the relationship is between the two variables. This coefficient ranges from -1 to 1. A value close to -1 means a strong negative relationship, while a value close to 0 means a weak relationship. Since -0.9153 is quite close to -1, it means there is a strong negative correlation.

Conclusion: Based on the strong negative correlation and the linear trend, Jazmin can conclude that using a linear model (the trend line) to represent her data is appropriate. This means that the linear relationship accurately describes how the two variables are related, and it can help her make predictions about one variable based on the other. So, Jazmin can confidently use this trend line to analyze her data!