Question

1. the mean weight of boys ages 2 - 12 is displayed in the table. the linear regression model ( y = 5.957x + 12.3 ) represents the data. use the model to predict the mean weight of boys age 5. the actual mean weight of boys age 5 is 40. determine the residual value for boys age 5. does this value indicate an overestimate or underestimate? explain.

Explanation:

Step1: Predict mean weight

Substitute \(x = 5\) into the linear regression model \(y=5.957x + 12.3\).

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Step2: Calculate residual

The formula for residual \(e=y_{actual}-y_{predicted}\). Here \(y_{actual} = 40\) and \(y_{predicted}=42.085\).

$$ e=40 - 42.085=- 2.085 $$

Answer:

The predicted mean weight is \(42.085\) lbs. The residual value is \(-2.085\). Since the residual is negative (\(e=-2.085<0\)), the model over - estimates the mean weight. A negative residual means the actual value (\(y_{actual} = 40\)) is less than the predicted value (\(y_{predicted}=42.085\)).