The simple linear regression model commonly seen is y = a + Bx + E (1) where x is a fixed variable (e.g., can be control

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The Simple Linear Regression Model Commonly Seen Is Y A Bx E 1 Where X Is A Fixed Variable E G Can Be Control 1 (72.23 KiB) Viewed 131 times

The simple linear regression model commonly seen is y = a + Bx + E (1) where x is a fixed variable (e.g., can be controlled), E(E) = 0 and 1(E) = 02. The OLS estimators for (a,b) based on n independent data (91,X1), ..., (yn,xn) are 2-1(-x)yi Σ(x-x)2 a = y - Bx (2) When x is a random variable, (1) can be considered as E(y|x) = a + Bx Also, (1) leads to y-a E =- B + B This is the inverse regression model from (1), where the new regression coefficients are and B If we estimate and by I and ž , respectively, using (2), is unbiased for? No. E) + . Likewise, Em * Exercises 1. Create a hypothetical data set and then perform simple linear regression analysis and the corresponding inverse regression analysis. 2. Construct unbiased estimators for the new intercept (i.e., m) and new slope (i.e.,) in the regression of x on y.