Unbiased estimate-Quant

[gargijain]

Referring to EXAMPLE 12 from CFAI, page 291-

Evaluating Economic Forecasts (2)

…If the forecasts are unbiased, the intercept, b₀, should be 0 and the slope, b₁, should be 1. We should also find E(Actual change – Predicted change) = 0. If forecasts are actually unbiased, as long as b₀= 0 and b₁ = 1, the error term [Actual change − b₀ − b₁(Predicted change)] will have an expected value of 0, as required by Assumption 3 of the linear regression model. With unbiased forecasts, any other values of b₀ and b₁ would yield an error term with an expected value different from 0.

Can someone pls explain why any other values of b₀ and b₁ would yield an error term with an expected value different from 0?

[gargijain]

Is it because if we have any other value for B₀ and B₁, then predicted variable will not be equal to actual ?

[S2000magician]

@gargijain

Is it because if we have any other value for B₀ and B₁, then predicted variable will not be equal to actual?

Yes.

[gargijain]

One more question…Can I say the following-

t test tests the correlation between 2 variables, where we test H₀: r = 0

t tests also tests slope coefficients, where H₀: b₁ = 1

f test tests whether all slope coefficients are zero, where H₀: b₁ = 0

[S2000magician]

@gargijain

One more question…Can I say the following-

t test tests the correlation between 2 variables, where we test H₀: r = 0

Yes.

@gargijain

t tests also tests slope coefficients, where H₀: b₁ = 1

You can test whether b_i is any value. The t-statistic given in an ANOVA table is for testing if b_i = 0.

@gargijain

f test tests whether all slope coefficients are zero, where H₀: b₁ = 0

H₀: b₁ = b₂ = ∙ ∙ ∙ = b_n = 0.