After using the quadratic model rather than the linear model, we found that the r^2 for the quadratic model is 0.876. What does this mean?
An R^2 value of 0.876 for the quadratic model suggests that approximately 87.6% of the variations in the dependent variable can be explained by the quadratic model. In other words, the quadratic model fits the data quite well, accounting for a significant portion of the variability.
The R-squared value, also known as the coefficient of determination, measures how well the quadratic model fits the data compared to the linear model. In this case, an R-squared value of 0.876 indicates that approximately 87.6% of the variation in the data can be explained by the quadratic model. This implies that the quadratic model provides a better fit to the data compared to the linear model, as it accounts for a higher proportion of the observed variability.
The coefficient of determination (r^2) is a statistical measure that indicates the proportion of the variance in the dependent variable that can be explained by the independent variable(s). In simple terms, it represents how well the quadratic model fits the data compared to the linear model.
A value of 0.876 for the r^2 in the quadratic model means that approximately 87.6% of the variance in the dependent variable can be explained by the independent variable(s) in the quadratic model. This suggests that the quadratic model provides a reasonably good fit to the data, explaining a significant portion of the variability.
To find the r^2 value for the quadratic model, you would typically perform a regression analysis, specifically a quadratic regression. This involves fitting a curve (rather than a straight line) to the data points and calculating the r^2 value based on the residuals (the differences between the actual values and the predicted values). Software packages like Excel, SPSS, or Python's scikit-learn library can be used to perform such regression analyses and obtain the r^2 value.