Question

We consider linear regression with known standard deviation ? = 1. After collecting 48 data points, we have the following summary statistics: ?_{i=1}^{48} X_i = -5.671304, ?_{i=1}^{48} Y_i = 33.06696, ?_{i=1}^{48} (X_i - X?)^2 = 44.12922, ?_{i=1}^{48} (Y_i - Y?)^2 = 236.5728 and ?_{i=1}^{48} (X_i - X?)(Y_i - Y?) = 88.99019. Predict the y-value Y_{49} that would be paired with a new x-value X_{49} = 3.

          We consider linear regression with known standard deviation
? = 1.
After collecting 48 data points, we have the following summary statistics:
?_{i=1}^{48} X_i = -5.671304, ?_{i=1}^{48} Y_i = 33.06696, ?_{i=1}^{48} (X_i - X?)^2 = 44.12922, ?_{i=1}^{48} (Y_i - Y?)^2 = 236.5728
and
?_{i=1}^{48} (X_i - X?)(Y_i - Y?) = 88.99019.
Predict the y-value
Y_{49}
that would be paired with a new x-value
X_{49} = 3.

We consider linear regression with known standard deviation
? = 1.
After collecting 48 data points, we have the following summary statistics:
?i=1^48 Xi = -5.671304, ?i=1^48 Yi = 33.06696, ?i=1^48 (Xi - X?)^2 = 44.12922, ?i=1^48 (Yi - Y?)^2 = 236.5728
and
?i=1^48 (Xi - X?)(Yi - Y?) = 88.99019.
Predict the y-value
Y49
that would be paired with a new x-value
X49 = 3.

Added by Miguel -Ngel A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/04/2023

Step 1

The formulas for b and a are: b = Σ(Xi - X)(Yi - Y) / Σ(Xi - X)^2 a = Y - bX We are given the following summary statistics: ΣXi = 5.671304 ΣYi = 33.06696 Σ(Xi - X)^2 = 44.12922 Σ(Yi - Y)^2 = 236.5728 Σ(Xi - X)(Yi - Y) = 88.99019 We also know that there are 48 Show more…

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We consider linear regression with known standard deviation. After collecting 48 data points, we have the following summary statistics: σ = 1. ∑ Xi = -5.671304, ∑ Yi = 33.06696, ∑ (Xi - X̄)² = 44.12922, ∑ (Yi - Ȳ)² = 236.5728, and ∑ (Xi - X̄)(Yi - Ȳ) = 88.99019. Predict the y-value Y49 that would be paired with a new x-value X49 = 3.