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Jade was working on her statistics homework one of the questions gave her a trend line and ask her to find the residuals she found the following residuals 2.6, 9.3, -5.489, and -6.59 what conclusion can Jade make about the linear model based on the residuals

A the linear model model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative be the line the linear module does not accurately represent the data since half of the residuals are positive and half of the residuals are negative see the linear model does not actually represent the data since the residual 9.3 means that the actual point is far from the estimate Dee the linear model seems to actually represent data since the residual 2.6 means that the actual point is not far from the estimate

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To evaluate Jade's residuals (2.6, 9.3, -5.489, and -6.59), we need to consider their implications regarding how well the linear model fits the data.

  1. Understanding Residuals:

    • A positive residual indicates that the actual value is greater than the predicted value (the model underestimates the actual value).
    • A negative residual indicates that the actual value is less than the predicted value (the model overestimates the actual value).

  2. Magnitude of Residuals:

    • The size of the residuals also matters. A larger absolute value of a residual (like 9.3 or -6.59) indicates that the prediction is less accurate for that data point.

Given this understanding:

  • The presence of some positive and some negative residuals does indicate a mix of overestimations and underestimations, but it does not inherently determine the adequacy of the linear model.
  • However, the residual of 9.3 is particularly significant, as it suggests a substantial deviation from the predicted value. This large positive residual indicates that one actual point is much higher than what the model estimates, suggesting that the linear model may not fit the data well.

Conclusion:

The best response regarding Jade's assessment of the linear model is: C - "The linear model does not actually represent the data since the residual 9.3 means that the actual point is far from the estimate."