The adjusted r^2 for the quadratic model is 0.9765 and the adjusted r^2 for the simple regression model is 0.94567.
What does this imply
This implies that the quadratic model explains a higher proportion of the variability in the data compared to the simple regression model. The adjusted r^2 value is a measure of how well the model fits the data, taking into account the number of predictors in the model. A higher adjusted r^2 indicates a better fit. Therefore, the quadratic model is a better fit for the data in this case.
The adjusted R^2 is a statistical measure used to determine the goodness of fit of a regression model. It takes into account the number of predictors in the model to provide a more accurate assessment of the model's performance.
In this case, we have two models: a quadratic model and a simple regression model. The adjusted R^2 value for the quadratic model is 0.9765 and the adjusted R^2 value for the simple regression model is 0.94567.
The adjusted R^2 ranges from 0 to 1, where a value closer to 1 indicates a better fit. Therefore, we can conclude that both models explain a significant amount of the variation in the dependent variable.
Based on the adjusted R^2 values, we can also compare the two models and make some observations. The adjusted R^2 for the quadratic model is higher than that of the simple regression model, indicating that the quadratic model provides a better fit to the data. This suggests that there may be a non-linear relationship between the predictors and the dependent variable, which is captured by the quadratic model.
However, it is important to note that the adjusted R^2 alone does not provide a complete understanding of the model's performance. Other factors such as the significance of the coefficients, the residuals, and the assumptions of the model should also be considered in the overall evaluation.
The adjusted r^2 is a statistical measure used to assess the goodness of fit for a regression model. It takes into account the number of variables in the model and adjusts the r^2 value accordingly.
In this context, the adjusted r^2 for the quadratic model is 0.9765, which indicates that approximately 97.65% of the variation in the dependent variable can be explained by the independent variable(s) included in the model. This implies that the quadratic model is able to capture a significant amount of the data's variation and provides a good fit to the observed data.
On the other hand, the adjusted r^2 for the simple regression model is 0.94567. This value indicates that around 94.567% of the variation in the dependent variable is explained by the single independent variable included in the model. While the simple regression model still provides a relatively good fit to the data, it is slightly less effective in capturing the variation compared to the quadratic model.
Overall, the higher the adjusted r^2 value, the better the model is at explaining the variation in the data. Therefore, an adjusted r^2 of 0.9765 for the quadratic model suggests a stronger fit compared to the adjusted r^2 of 0.94567 for the simple regression model.