For the SLR model y = Bo+Bxiui, with y; as the IBM stock return and x,...

 

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For the SLR model y₁ = Bo+B₁xiui, with y; as the IBM stock return and x, as the market return (CAPM) that are both in original units, e.g., 0.05 means 5% monthly return. = • Show that Avi B₁, i.e., the slope coefficent captures the units of changes in y corresponding to one unit change of xi ⚫ Suppose we only change the unit of x, to percentage points, i.e., the market return x; will be 5 for the 5% monthly return. Does this change the values of Bo, and B₁? If so, by how much? ⚫ Suppose we only change the unit of y, to percentage points, i.e., the IBM stock return y; will be 5 for the 5% monthly return. Does this change the values of B0, and ₁? If so, by how much? ⚫ Do the two changes of units above make R² different? Use the definition of R² to prove it. 3. (2/10) For the SLR model y = B₁x+u, i.e., regrssion without intercept, • Use the OLS principal to derive the OLS estimator of B₁ 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? For the SLR model y₁ = Bo+B₁xiui, with y; as the IBM stock return and x, as the market return (CAPM) that are both in original units, e.g., 0.05 means 5% monthly return. = • Show that Avi B₁, i.e., the slope coefficent captures the units of changes in y corresponding to one unit change of xi ⚫ Suppose we only change the unit of x, to percentage points, i.e., the market return x; will be 5 for the 5% monthly return. Does this change the values of Bo, and B₁? If so, by how much? ⚫ Suppose we only change the unit of y, to percentage points, i.e., the IBM stock return y; will be 5 for the 5% monthly return. Does this change the values of B0, and ₁? If so, by how much? ⚫ Do the two changes of units above make R² different? Use the definition of R² to prove it. 3. (2/10) For the SLR model y = B₁x+u, i.e., regrssion without intercept, • Use the OLS principal to derive the OLS estimator of B₁ 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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1 AB1 captures the change in y IBM stock return corresponding to a 1 unit change in x market return ... View the full answer