A random sample of people who tried 3 types of diet is collected to determin if mean weight loss differs across diet types.

Assume the result of inference before taking age as a covariate shows no significant evidence proving differences of mean weight loss across 3 diet types.

However, it shows there is significant evidence that there are differences of mean weight loss, when performing ANCOVA taking age as a covariate.

Calculate Least-squares means of weight loss among 3 diet types. What is the Least-squares means of weight loss for type1 diet?

Weight Loss: (6.3789, 6.3055, 3.669, 6.0259, 4.9472, 14.9425, 15.5144, 14.2381, 10.4763, 11.21, 10.8994, 14.8156, 14.8724, 16.9924, 17.0841)

Diet Type: ('type1', 'type1', 'type1', 'type1', 'type1', 'type2', 'type2', 'type2', 'type2', 'type2', 'type3', 'type3', 'type3', 'type3', 'type3')

Age: (20, 20, 24, 24, 23, 40, 40, 39, 36, 39, 55, 54, 53, 54, 53)