Data analysis - Formulario

Y VALUE OF·i ̂(7) e = Y - Yi i i2e(8) → [Σ ]AL VALUESiCompute :‣ 2∑ e column (8)i2 used to compute and̂ ̂̂σ = = v a r (b) v a r (a)→• u n − 2 n − 2 [2 = =NUMBER OF PARAMETER α; β]Signi cance of β-- Signi cance of :βH : = 0 (vs H : 0)β β ≠0 1 b − 0* bTested with soT = ∼ t R : {x , y : > t }• n−2 1−α/2;n−2̂ ̂v a r (b) v a r (b)tFind the interval by computing the value of for = 0.05 | = 0.01 | = 0.10α α α α1− ;n−22* b - 0 if H = 0→ 0✦ b - n if H = n→ 0 2 - 5fi fi fi fiCompute‣ 2̂σ bû T =v a r (b) = obs2∑ (X − X̄ ) ̂v a r (b)iAccept H if T falls in the interval [- ; +]→ … …0 obsSigni cance of α-- Signi cance of :αH : = 0 (vs H : 0)α α ≠0 1 a − 0 aTested with soT = ∼ t R : {x , y : > t }•

1−α/2;n−2n−2̂ ̂v a r (a) (a) v a r (a)= 0.05 | = 0.01 | = 0.10 [the same as before as distribution is t ]α α α 2Compute‣ [ ]2 a1 X̄2̂ ̂ T =v a r (a) = σ + obsu n 2∑ (X − X̄ ) ̂v a r (a)iAccept H is T falls in the interval→ 0 obsWhat to do next-- If H : = 0 and H : = 0 are both rejected, ok! go to next step!β α0 0- If H : = 0 is not rejected, stop and look for another explicative variable to replace X which is notβ0signi cantly effective on Y- If H : = 0 is rejected and H : = 0 is acceptedβ α0 0The model Y = + X + u is not correctα β‣ Specify the model Y = X + u’↪︎ [ = 0]β’ WITHOUT SINCE IT ISα• Add column(9) X Y → [Σ ]· AL VALUESi i2(10) → [Σ ]X AL VALUESi b’USED TO COMPUTE✦ ̂(11) = b’ • xY′i ̂(12) e’ = Y - Y′i i2(13) e' → [Σ ]AL VALUESiUSED FOR SIGNIFICANCE

ANALYSIS

Calculate the OLS estimator b’‣ ∑ X Y column (9)i ib′ = =• 2∑ X column (10)iY = b’ x + e’ estimated statistical model→̂ = b’ x estimated regression line (scatter plot)Y →'And then again step 3 [ ]

SIGNIFICANCE ANALYSIS

check again the signi cance of by testing H : = 0 (vs H : 0)↪︎ β’ β’ β’ ≠0 12∑ e' i2̂σ = [1 = = ]

NUMBER OF PARAMETER Βu′ n − 1 2̂σ b′u′̂v a r (b′) = T =obs(b′ )2∑ X ̂v a r (b′)i t

Find the interval by computing the value of for = 0.05α α1− ;n−2‣ 2

Check if T is falls inside the interval (↑) if accepted than we can go on to step 4b

4. Compute R̄ 2- R̄- Calculate (speci c of the model you estimated and validated in step 2 and 3).2R̄

The is very satisfactory if its value is larger than 90%2 3 - 5    fi fi fi fi fi