Regression model: 𝑦 = 𝑎+ 𝑏𝑥+ 𝜖. Suppose that 𝑥 and 𝜖 are random
Posted: Tue Apr 12, 2022 10:54 am
Regression model: π¦ = π+ ππ₯+ π.
Suppose that π₯ and π are random variables, and parameters π and
π are constants.
Suppose that the i.i.d samples (π₯1,β¦,π₯π) are realizations of the
random variable π₯, and suppose that π₯ and π are independent. Given
that
πππ(π₯)=πΈ[π₯βπΈ(π₯)]2= 1πΞ£(π₯πβπ₯Μ )2ππ=1
πΆππ£(π₯,π¦)= πΈ[(π₯βπΈ(π₯))(π¦βπΈ(π¦))]=1πΞ£(π₯πβπ₯Μ )(π¦πβπ¦Μ )ππ=1,
Try to establish the expression for the estimator π.
Suppose that π₯ and π are random variables, and parameters π and
π are constants.
Suppose that the i.i.d samples (π₯1,β¦,π₯π) are realizations of the
random variable π₯, and suppose that π₯ and π are independent. Given
that
πππ(π₯)=πΈ[π₯βπΈ(π₯)]2= 1πΞ£(π₯πβπ₯Μ )2ππ=1
πΆππ£(π₯,π¦)= πΈ[(π₯βπΈ(π₯))(π¦βπΈ(π¦))]=1πΞ£(π₯πβπ₯Μ )(π¦πβπ¦Μ )ππ=1,
Try to establish the expression for the estimator π.