Linear Econometrics代写 Finance代写

BU.232.620 (Linear Econometrics for Finance)

Linear Econometrics代写  Suppose we only change the unit of xi to percentage points, i.e., the market return xi will be 5 for the 5% monthly return.

Homework 2  Linear Econometrics代写

1.For the simple linear regression (SLR) model yi = β₀ + β₁x_i + u_i , with yi as the IBM stock return and xi as the market return (CAPM) that are both in original units, e.g.,0.05 means 5% monthly return.

•  Suppose we only change the unit of x_i to percentage points, i.e., the market return x_i will be 5 for the 5% monthly return. Does this change the values of β₀ , and β₁? If so, by how much?
•  Suppose we only change the unit of y_i to percentage points, i.e., the IBM stock return y_i will be 5 for the 5% monthly return. Does this change the values of β₀,and β₁? If so, by how much?
•  Do the two changes of units above make prove it. R2 di§erent? Use the deffnition of R² to prove it.

2.For the SLR model yi = 1xi + ui , i.e., regrssion without intercept,  Linear Econometrics代写

Use the OLS principal to derive the OLS estimator of β₁ for this model.

Compare the OLS estimator for this regression with that for the regression with intercept. Under what conditions are the two estimators equal to each other?

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