2. (12' 3'+2' +2' +2+3) Consider the model Yt= a + x + t, t= 1,...,...

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2. (12' 3'+2' +2' +2+3′) Consider the model Yt= a + x₂ß + εt, t= 1,..., T where xt is kx 1. Let x = (₁,,T)' (hence r is the giant matrix without the column of 1's), e = (1,¹,ET)'. Assume E[ex] = 0, and E[ɛɛ¹|r] =o²1. Let 3 be the OLS estimate of 3. Suppose we now multiply all the observation values (yt, t) by X>0 and estimate the model again by OLS. Let 3 be the new OLS estimate after multiplying all the observations by A. Answer the questions below and show your work. a). How much is compared with ? (Hint: the partial regression formulas would be helpful, for 3 here does not include the intercept.) b). How much is a compared with â? (Hint: use the fact that y = a + 'ß in both old and new data.) c). Does the R² change (and if so, by how much)? d). Does the vector of estimated residuals & = yt-â-xß change (and if so, by how much)? e). Does the value of t statistic for Ho : 3 = 0 change (and if so, by how much)? 2. (12' 3'+2' +2' +2+3′) Consider the model Yt= a + x₂ß + εt, t= 1,..., T where xt is kx 1. Let x = (₁,,T)' (hence r is the giant matrix without the column of 1's), e = (1,¹,ET)'. Assume E[ex] = 0, and E[ɛɛ¹|r] =o²1. Let 3 be the OLS estimate of 3. Suppose we now multiply all the observation values (yt, t) by X>0 and estimate the model again by OLS. Let 3 be the new OLS estimate after multiplying all the observations by A. Answer the questions below and show your work. a). How much is compared with ? (Hint: the partial regression formulas would be helpful, for 3 here does not include the intercept.) b). How much is a compared with â? (Hint: use the fact that y = a + 'ß in both old and new data.) c). Does the R² change (and if so, by how much)? d). Does the vector of estimated residuals & = yt-â-xß change (and if so, by how much)? e). Does the value of t statistic for Ho : 3 = 0 change (and if so, by how much)?

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a The OLS estimate of beta denoted by hat beta is given by hat beta XX1Xy If we multiply all the observation values by lambda 0 the new data becomes y... View the full answer