You are given the following data, where X₁ (hours of professional development) and X₂ ( aptitude test scores) are used to predict Y (annual salary in thousands):

Y X₁ X₂

40 100 10

50 200 20

50 300 10

70 400 30

65 500 20

65 600 20

80 700 30

Determine the following values intercept, b₁, b₂, SS_res, SS_reg, F, s^2, S_{res, S (b}1), S(b²), t_1,t2

Please, can you show me the hand calculations of the following solutions on the problem?

Intercept = 28.095

b₁ = 0.038

b₂ = 0.833

SS_res = 21.429

SS_reg = 1128.571

F = 105.333

s² = 5.357

s_res = 2.315

s_b1 = 0.0058

s_b2 = 0.1543

t₁ = 6.532

t₂ = 5.401