These both play a large roll in Statistics.  A scatter plot helps us to see the relationship/association involved in bivariate (data sets with more than one variable.)  Regression analysis is useful for modeling data sets with equations to help make predictions.

Scatter Plots

Scatter plots are a means of graphing bivariate (two variables) data to see relationships or associations between the two variables. They can have positive linear correlation, negative linear correlation, no correlation, or non linear association. The strength of the association is dependent on the variability of the plotted points. Technology can be used to find the correlation coefficient of the scatter plot for linear data.

Scatter Plot and Correlation Coefficient in TI-84
Scatter Plot and Correlation Coefficient in TI-Nspire
Scatter Plot in Excel 2016

Linear Regression

Linear regression is used when the scatter plot shows a linear relationship. If the scatter plot shows a general linear trend,
a regression equation is used. We can use the regression equation to make predictions. When making predictions, avoid extrapolating (reaching beyond the known data), because often these predictions can be very wrong.

Line of Best Fit and Making Predictions in TI-84
Linear Regression and Making Predictions in the TI-Nspire

Nonlinear Regression

Sometimes linear regression is not the best model. We can use other types of modeling, or we can change the datat to fit become more linear by straightening it out using logarithms, roots, or powers.

Linear vs Exponential in TI-84