Suppose we use a person\'s dad\'s height to predict how short or tall the person

Question

Suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows:

Least Squares Linear Regression of Height

Predictor
Variables Coefficient Std Error T P
Constant 20.2833 8.70520 2.33 0.0223
DadsHt 0.67499 0.12495 5.40 0.0002

R² 0.2673 Mean Square Error (MSE) 23.9235
Adjusted R² 0.2581 Standard Deviation 4.9000

Interpret the standard deviation in this problem.

We expect most of the sampled heights to fall within 4.9 inches of their least squares predicted values.

We expect most of the sampled heights to fall within 9.8 inches of their least squares predicted values.

We expect most of the sampled dad's heights to fall within 4.9 inches of their least squares predicted values.

Explanation / Answer

Here, the correct interpretation of the standard deviation is,

We expect most of the sampled dad's heights to fall within 4.9 inches of their least squares predicted values.

it could be any side of the predicted line but within 4.9 inches from the line.

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