To determine which regression equation best matches the scatterplot, I will analyze the overall shape and trend of the data in the scatterplot. Based on visual analysis, here are some observations about the scatterplot:

1. Behavior of Data:

   • The data shows a nonlinear relationship.
   • For smaller $x$-values (negative $x$), the $y$-values are decreasing.
   • Around $x = 0$, the data begins to increase.
   • For larger $x$-values (positive $x$), the increase in $y$ accelerates significantly.

2. Possible Regression Models:

   • This trend suggests that the data could best fit an exponential regression model or quadratic regression model.
   • A linear model would not work, as the data is clearly curved.
   • A logarithmic model would not work because the $y$-values are both increasing and decreasing, which doesn't match a logarithmic trend.

Please provide the specific regression equations or models as answer options, so I can compare and determine the best match. If you don't have specific options, I can give a general suggestion based on the trends observed in the scatterplot.

Would you like me to assist further with detailed steps or provide other clarifications?

Follow-up Questions:

1. Can you share the regression equations provided in the question?
2. Do you know if the regression is being calculated for an exponential, quadratic, or polynomial model?
3. Is there a specific context (e.g., physical phenomena or experimental data) for the scatterplot?
4. Would you like an explanation of the differences between regression models?
5. Should I explain how to calculate regression equations using software or graphing tools?

Tip:

When identifying regression models, always compare the shape of the scatterplot to known function types (linear, quadratic, exponential, etc.) to narrow down your options quickly.