Question

In a linear regression with a single continuous predictor and 100 data points, the residual degrees of freedom are ________ (Answer in integer).

Hint:

For simple linear regression, the residual degrees of freedom are calculated as \( n - 2 \), where \( n \) is the number of data points.

Answer 1

Correct Answer: 98

In a linear regression model, the residual degrees of freedom are calculated as: \[ \text{Residual degrees of freedom} = n - p - 1, \] where \( n \) is the number of data points and \( p \) is the number of predictors. Here, \( n = 100 \) and \( p = 1 \) (since there is a single continuous predictor). Thus, the residual degrees of freedom are: \[ \text{Residual degrees of freedom} = 100 - 1 - 1 = 98. \] Thus, the residual degrees of freedom are \( 98 \).