For Northfield (β̂₁ = 2.0659, s = 9.642, SS_xx = 4,531.875, n = 8), compute SE(β̂₁), the slope t and its df, and decide at the 1 % level two-sided using t₀.₀₀₅;₆ = 3.707.
For Northfield (β̂₁ = 2.0659, s = 9.642, SS_xx = 4,531.875, n = 8), compute SE(β̂₁), the slope t and its df, and decide at the 1 % level two-sided using t₀.₀₀₅;₆ = 3.707.
Answer
import math b1, s, ss_xx, n = 2.0659, 9.642, 4531.875, 8 t_crit = 3.707 # t(0.005; 6), two-sided at 1 % se_b1 = s / math.sqrt(ss_xx) t = b1 / se_b1 decision = "reject H0" if abs(t) > t_crit else "do not reject H0" print(f"SE(b1)={se_b1:.4f} t={t:.2f} df={n - 2} decision={decision}")
IBS1 §13.4 (S_b₁ and the slope t), CC BY 4.0; BCc ch 8 (the slope test); H-W3 (R’s t value line); original dataset