Assume a balanced design with a single quantitative factor with `a' equally

spaced observed levels.

(a)Show that the grand sample mean ybar.. is the estimate of Beta₀ mentioned in the screenshot below.

(b) Derive the estimates of Beta_i for i = 1, 2,... a - 1 mentioned on

the same screenshot.

. Want to fit the model f (t) = Bo + B1 Pi(t) + B2P2(t) + B3P3(t) + BAPA(t) . Estimation and Testing - B1: use I1. B1 = Clly1. + ... + Cisys. D1 Test: Ho : 81 = 0, Flo = SSCAN FI,N-5. MSE - B2: use I'2, B2 = C2191. + . . . + 0257/5. D2 Test: Ho : 2 = 0, F20 = SSCAN Fi,N-5 MSE - Similar for 83 and B4 . Question: what is the estimate for Bo