To assess whether the estimated regression equation provides a good fit, we need the adjusted R² value. The adjusted R² measures the proportion of variation in the dependent variable (selling price, $y$) that is explained by the independent variables (bathrooms, square footage, and bedrooms) after adjusting for the number of predictors in the model. Here's how you can approach this:

Steps:

1. Calculate the total variation ($SST$), which is the sum of squared deviations of the actual selling prices from their mean.
2. Calculate the explained variation ($SSR$), which is the sum of squared deviations of the predicted selling prices ($\hat{y}$) from the mean of the actual selling prices.
3. Calculate the residual variation ($SSE$), which is the sum of squared deviations of the actual selling prices from the predicted selling prices.
4. Use the formula for $R^2$: $R^2 = \frac{SSR}{SST}$
5. Adjust $R^2$ to account for the number of predictors ($k$) and sample size ($n$) using the formula: $\text{Adjusted } R^2 = 1 - \left( \frac{SSE / (n - k - 1)}{SST / (n - 1)} \right)$

Without the exact data for residuals and means, we cannot compute the adjusted $R^2$ directly here. However, if you provide the adjusted $R^2$, we can assess whether it is close to 1 (indicating a good fit) or not.

General Interpretation Guidelines:

• If Adjusted $R^2$ is close to 1: The model provides a good fit, explaining a large portion of the variance in selling prices.
• If Adjusted $R^2$ is much lower: The model does not fit the data well, and additional predictors or a different model may be needed.

Would you like me to help compute $R^2$ or adjusted $R^2$ using specific values, or do you have additional details to provide?

5 Related Questions:

1. How is adjusted $R^2$ different from $R^2$, and why is it preferred in regression analysis?
2. Can we use this regression equation to predict selling prices for houses with extreme values (e.g., very high or low square footage)?
3. How sensitive is the selling price prediction to the number of bathrooms compared to the square footage?
4. What assumptions are made when using multiple regression models like this one?
5. What steps can be taken to improve the model's fit if adjusted $R^2$ is low?

Tip:

Always visually inspect the residual plots to check for patterns that might indicate violations of regression assumptions, such as non-linearity or heteroscedasticity.