# How to test if the effects of two covariates are statistically different?

I'm trying to model eating behavior with this model: $y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_3+\beta_4x_4+ϵ$

where y is BMI and the parameters are various characteristics of the food/drink a person orders.

Drink size is represented by $\beta_1$ and $\beta_2$ like so:

• $\beta_1$ can take two values: 1 for large and 0 for not large.
• $\beta_2$ can also take two values: 1 for medium and 0 for not medium.
• If both $\beta_1$ and $\beta_2$ are 0, this represents small.

How do I test if the influence of small drinks on BMI is the same as the influence of large drinks? I would usually proceed like so (the betas do not correspond with the one in the model above):

$H_0: \beta_{small} = \beta_{large} \\ H_A: \beta_{small} \ne \beta_{large}$

but the thing is, small drinks are not directly represented in any parameter.

• Small is your reference category so the other two coefficients (for medium and large) are the difference between small and their respective predictor. Dec 22 '17 at 16:33
• Also, you might want to represent drink size with a single variable instead of two separate variables.
– mkt
Dec 22 '17 at 16:36