Question

A linear regression model was fitted to a set of \( (x, y) \) data. The total sum of squares and sum of squares of error are 1200 and 120, respectively. The coefficient of determination \( R^2 \) of the fit is ......... (rounded off to one decimal place).

Hint:

The coefficient of determination \( R^2 \) indicates the goodness of fit of a model. A higher \( R^2 \) value means the model explains a greater proportion of the variance in the data. An \( R^2 \) of 0.9 means that 90% of the data's variability is explained by the model.

Answer 1

The coefficient of determination \( R^2 \) is a statistical measure that indicates the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It can be calculated as: \[ R^2 = 1 - \frac{SSE}{SST} \] Where:
- \( SSE \) is the sum of squares of error (120),
- \( SST \) is the total sum of squares (1200).
Substituting the given values: \[ R^2 = 1 - \frac{120}{1200} = 1 - 0.1 = 0.9 \] Thus, the coefficient of determination \( R^2 \) of the fit is \( \mathbf{0.9} \), meaning 90% of the variance in the data is explained by the regression model.