RSS, OLS Residuals

From a cross-section sample on average costs (C) and output (O) for 30
firms (10 small, 10 medium and 10 large) the following OLS estimates
were obtained;

All Ci = 35.8 - 0.961Oi + e1i R2=0.61, RSS=1184.8

(13.0) (-6.7)

Small Ci = 54.8 - 2.78Oi + e2i R2=0.97, RSS=21.57

(34.0) (-15.2)

Medium Ci = 22.5 - 0.56Oi + e3i R2=0.70, RSS=14.67

(10.2) (-4.3)

Large Ci = 1.47 + 0.42Oi + e4i R2=0.69, RSS=8.12

(0.55) (4.2)

, j= 1,4 are OLS residuals.

a) How do I Interpret the estimated equations and use an F Test to test
the hypothesis that there is no difference in the cost functions for
small, medium and large firms. What assumptions does this test require?
Is there any evidence given above that these assumptions are violated
and how would I explain this?

(b) How can I plot the estimated functions for small, medium and large
firms with Output varying between 0 and 25. What conclusions can I
draw from this?

(c) Would it make sense to estimate the model connecting average costs
and output for all firms by including dummy variables? Explain.