The quadratic model is most appropriate to fit the data.
The quadratic model has a higher R-squared value than the linear model, which means that it explains more of the variation in the data.
The residual plot for the quadratic model is more evenly distributed around zero than the residual plot for the linear model, which suggests that the quadratic model is a better fit for the data.
The data itself shows a clear quadratic trend. The distance traveled by the toy car increases at a faster and faster rate as the pull-back distance increases. This is consistent with the quadratic model, which predicts that the distance traveled will increase proportional to the square of the pull-back distance.
Here is a more detailed explanation of each point:
R-squared value: The R-squared value is a measure of how well a model fits the data. It ranges from 0 to 1, with higher values indicating a better fit. The R-squared value for the quadratic model is 0.923, while the R-squared value for the linear model is 0.881. This means that the quadratic model explains 92.3% of the variation in the data, while the linear model only explains 88.1% of the variation.
Residual plot: The residual plot is a graph of the residuals, which are the differences between the actual values of the dependent variable and the predicted values of the dependent variable. A well-fitting model will have residuals that are evenly distributed around zero. The residual plot for the quadratic model is more evenly distributed around zero than the residual plot for the linear model. This suggests that the quadratic model is a better fit for the data.
Quadratic trend in the data: The data itself shows a clear quadratic trend. The distance traveled by the toy car increases at a faster and faster rate as the pull-back distance increases. This is consistent with the quadratic model, which predicts that the distance traveled will increase proportional to the square of the pull-back distance.
Overall, the quadratic model is the most appropriate model to fit the data because it has a higher R-squared value, a more evenly distributed residual plot, and it is consistent with the quadratic trend in the data.