Helght and Weight Using the data in the Studentsurvey dataset containing the students' weight and height, we use technology to find that a regression line to predict weight (in pounds) From height (in inches) is \[ \text { Weight e }=170+4 . H 2 \text { (Ileinhi) } \] Click here for the dataset associated with this question. (d) Wilat weight does the regression line predict for a baby who is 20 inches long? Round your answer to one decimal place. \[ \text { Weight }= \] \( \square \) \( \square \) pounds Why is it not appropriate to use the regression line in this case? It is because \( \square \) (Ctif) *

To solve the problem, we will follow these steps: 1. **Extract the known conditions**: - The regression line equation is given as: \[ \text{Weight} = 170 + 4H^2 \] - We need to predict the weight for a height \( H = 20 \) inches. 2. **Substitute the height into the regression equation**: - We will substitute \( H = 20 \) into the equation to find the predicted weight. 3. **Calculate the predicted weight**: - The calculation will be done step by step. Let's perform the substitution and calculation: \[ \text{Weight} = 170 + 4(20^2) \] Calculating \( 20^2 \): \[ 20^2 = 400 \] Now substituting back into the equation: \[ \text{Weight} = 170 + 4(400) \] Calculating \( 4(400) \): \[ 4(400) = 1600 \] Now, adding this to 170: \[ \text{Weight} = 170 + 1600 = 1770 \] Thus, the predicted weight for a baby who is 20 inches long is: \[ \text{Weight} = 1770 \text{ pounds} \] Now, rounding to one decimal place, we have: \[ \text{Weight} = 1770.0 \text{ pounds} \] ### Why is it not appropriate to use the regression line in this case? It is not appropriate to use the regression line for a baby who is 20 inches long because: - The regression model is likely based on data from older children or adults, and using it to predict the weight of a baby falls outside the range of the data used to create the model. This can lead to inaccurate predictions, as the relationship between height and weight may not hold for infants. Thus, the final answers are: \[ \text{Weight} = 1770.0 \text{ pounds} \] And the reason is: It is because **the regression model is not valid for predicting weights of infants, as it is based on data from older individuals.**