1. For the data point $(3, 10)$, what is the residual for the quadratic model $y = x^2 - x + 3$? The residual is ___.
2. When analyzing a residual plot for a quadratic regression, which observation suggests that the quadratic model is a good fit for the data?
3. A quadratic model $y = -x^2 + 3x + 2$ is used to fit a set of data. If one of the actual data points is $(2, 5)$, the corresponding residual is ___.
4. A statistician creates a residual plot after fitting a quadratic model to a dataset. If the plot shows a distinct curved pattern, what is the most likely conclusion?
5. A residual plot is created for the model $y = x^2 + x$. For the data point $(4, 22)$, the corresponding point on the residual plot is $(4, \text{\_\_\_})$.
6. A quadratic regression model has a coefficient of determination of $R^2 = 0.88$. What does this value indicate about the model?
7. If a quadratic model has a coefficient of determination of $R^2 = 0.97$, what percentage of the variation in the data does the model explain? The answer is ___%.
8. A researcher creates two models for a dataset. Model A has $R^2 = 0.91$ and Model B has $R^2 = 0.65$. Which statement correctly compares the two models?
9. A student performs a quadratic regression and finds that $R^2 = 0.35$. What is the most appropriate conclusion to draw?
10. For a set of data points that lie perfectly on a parabola, what would be the coefficient of determination, $R^2$, for the quadratic model? The value would be exactly ___.