The value of $R^2$ (the coefficient of determination) measures the proportion of the variation in the dependent variable that is explained by the least squares regression model.

Steps to Solve:

1. Interpret $R^2$:

   • $R^2 = \frac{\text{Explained Variation}}{\text{Total Variation}} \times 100\%$.
   • It is often expressed as a percentage and represents how well the independent variables explain the dependent variable.

2. Context:

   • This percentage relates to the dependent variable because $R^2$ measures the fit of the model to the actual outcomes (y-values).

3. Answer:

   • The statement implies:

     The $R^2$ value shows that the least squares model explains approximately $R^2 \times 100\%$ of the total sample variation in the dependent variable.

   • Round the calculated percentage to one decimal place if provided with $R^2$. If you do not have the value, it needs to be given or calculated.

Would you like to provide $R^2$ so I can calculate the exact percentage for you?

Follow-Up Questions:

1. What is the given value of $R^2$, if available?
2. Are you looking for clarification on how $R^2$ is derived or used in regression analysis?
3. Would you like an explanation of the relationship between $R^2$ and the dependent variable?
4. Are you curious about the limitations of $R^2$ in model evaluation?
5. Would you like to learn about how $R^2$ is influenced by additional variables in a model?

Tip: Always verify whether the $R^2$ value is adjusted ($\text{Adjusted } R^2$) or unadjusted to avoid overestimating the model's explanatory power when additional predictors are involved.