# Unbiased estimate-Quant

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 − b0b1(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?

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

Yes.

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

Yes.

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

H0: b1 = b2 = ∙ ∙ ∙ = bn = 0.