Final answer:
The matching condition for a scatterplot of X2 on X is D. Nonlinear effect, which indicates the possibility of a nonlinear relationship between the variables and the potential need for a nonlinear model.Option D is the correct answer.
Step-by-step explanation:
The student's question asks to match a scatterplot of X2 on X with a condition that can be tested, a test statistic, or an estimate. In this scenario, the correct answer is D. Nonlinear effect. A scatterplot of X2 on X would typically be used to investigate whether there is a nonlinear relationship between X and X2, hinting that the model may require a transformation due to nonlinearity of the data. This type of plot can help determine if a quadratic or another type of nonlinear model should be considered.
If the scatterplot shows a clear curve, it implies that a simple linear regression model with the independent variable X might not be adequate, and hence the nonlinear relationship between the variables must be accounted for in the analysis. Other choices, such as similar variances, partial slope for X, or calibration plot, do not directly relate to the pattern of the scatterplot in relation to nonlinearity. Collinearity could be a concern in multivariate regression, but the given scatterplot is a bivariate plot between X and X2, and does not typically indicate collinearity.