Dummy variables and interaction

[Nikkip23]

Hi all,

For my thesis I am doing an regression on two dummy variables.
Dummy for size consists of three options, large, medium and small:
- Large = 1 if large, otherwise 0
- Small = 1 if small, otherwise 0
- Medium is captured in the alpha (β_0)

And, dummy for height has two option, high or low:
- High = 1 if high, otherwise 0
- Low is captured in the alpha (β_0)

Model: Y= β_0+β_1 Large+β_2 Small+β_3 High+β_4 Large*High+β_5 Small*High +ε_i

I included interaction terms for these dummies: Large*High and Small*High

Assume the following coefficients:

Large 0.0326**
Small 0.0116
High 0.0207**
Large*high -0.0347
Small*high -0.0137*
Constant 0.0276**

Can I interpret these results the following:
Being large significantly increases the Y by 0.0326 more compared to medium firms (β_0)
Being small increases the Y by 0.0116 more compared to medium firms (non-significant)
Being high significantly increases the Y by 0.0207 more compared to low firms (β_0)
Being large and high decreases the Y by -0.0347 more than being medium and low firms (non-significant)
Being small and high significantly decreases the y by -.0137 more compared to medium and low firms
Being medium and low significantly increases the Y by 0.0276

Or should I add the coefficients in the following way in order to interpret them:

Medium – Low = β_0
Medium – High = β_0+ β_3
Large – Low = β_0+ β_1
Large – High = β_0+ β_1+β_3+β_4
Small – Low = β_0+ β_2
Small – High = β_0+ β_2+β_3+ β_5

Thank you in advance!

Nikki