In a full 2^k factorial experiment for the study of the effects of combinations of three fertilizer types, N, K, and P each at two levels, on the growth of sweet potatoes; the following data show the weights of good sweet potatoes picked for plots of the same size following applications of fertilizer. The experiment was replicated three times:  Obtain the factorial effects and hence analyze the data fully. Check for violations of assumptions.

(1) 39.63 41.27 40.22 k n 56.08 54.86 45.37 33.75 33.26 38.25 nk 50.83 50.63 51.93 p 42.47 53.94 47.94 kp 59.84 51.43 50.96 54.49 53.32 40.31 npk 63.1 49.49 48.97