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 the mean weight

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

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Step2: Calculate the residual

The formula for the residual \(e\) is \(e=\text{Actual value}-\text{Predicted value}\).
Given the actual value \(y_{actual}=40\) and the predicted value \(y_{predicted} = 42.085\).

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

Answer:

The predicted mean weight of boys age \(5\) is \(42.085\) lbs. The residual value is \(-2.085\). Since the residual \(e=-2.085<0\) (actual value \(40\) is less than the predicted value \(42.085\)), the model over - estimates the mean weight of 5 - year - old boys.