5. the mean weight of boys ages 2 - 12 is displayed in the table. the linear regression model ( y = 5.957x +…

5. 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.

5. 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.

Answer

Explanation:

Step1: Predict mean weight

Substitute (x = 5) into the linear regression model (y=5.957x + 12.3). [ \begin{align*} y&=5.957\times5+12.3\ &=29.785 + 12.3\ &=42.085 \end{align*} ]

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)).