You are analyzing customer data to decide which statistical methods are most useful for understanding behavior. In a sample of 1,200 customers, 480 are repeat purchasers and 720 are one-time purchasers. The repeat group has an average annual spend of $186 with a standard deviation of $72, while the one-time group has an average annual spend of $164 with a standard deviation of $68. You also fit a simple linear model of annual spend against email engagement rate and estimate a slope of 42.5 dollars per 1.0 increase in engagement rate, with a standard error of 10.8.
Which statistical methods would you use here, and based on the results, what can you conclude about differences between customer groups and the relationship between engagement and spend?