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Question

Four points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 17 in increments of 1. A line is drawn that almost passes through all the points.

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 should conclude that the linear model she found is appropriate for the dataset she graphed. The correlation coefficient of -0.9153 indicates a strong negative linear relationship between the two variables in her dataset. This means that as one variable increases, the other tends to decrease in a consistent manner.

Additionally, the fact that the trend line equation is close to the data points suggests that the linear model is fitting the data well. A strong correlation coefficient (closer to -1) generally indicates that a linear model is a suitable representation of the data, and the negative value confirms the direction of the relationship.

In summary, given the strong correlation coefficient and the reasonably fitting trend line, Jazmin can conclude that using a linear model to describe her data is appropriate.