Consider a set of equity returns from four different markets across 12 different periods. The data are available in the marketdata.txt. Define the forth variable as your response variable (Y). Define the following three models: Model 1 Model 2 Model 3 Y = Bo + ₁1 + Ei; Y = Bo + B₂21 + Ei Y₁ = Bo + Bizi + B₂x2i + Ei What could you say about the significance of the parameters in the three models? Are the data satisfying the normality assumption in each model? The adjusted R² tells us which is the best model, when we have different number of exogenous variables across the models. As for the R2, the model with the highest adjusted R² is the best. By using the adjusted R2, state which is the best 1-13 Mkt 1 Mkt 2 Mkt 3 Mkt_4 0.0083 0.0427 -0.0179 -0.0039 -0.0012 -0.0372 0.0090. -0.0026 -0.0549 -0.0521 -0.0462 -0.0567 0.0275 -0.0626 0.0338 0.0140 -0.0568 -0.0737 -0.0521 -0.0505 -0.0370 -0.0160 -0.0234 -0.0266 0.0575 0.0508 0.0603 0.0548 0.0103 -0.0138 0.0237 0.0147 0.0069 -0.0017 0.0038 -0.0010 -0.0403 -0.0326 -0.0304 -0.0259 0.0054 0.0222 0.0142 0.0137 0.0303 0.0947 0.0295 0.0299

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Consider a set of equity returns from four different markets across 12 different periods. The data are
available in the marketdata.txt. Define the forth variable as your response variable (Y). Define the
following three models:
Mkt_1
0.0083
-0.0012 -0.0372 0.0090
-0.0549 -0.0521 -0.0462 -0.0567
Mkt 2
0.0427
Mkt_3 Mkt4
-0.0179 -0.0039
• Model 1 Y; = Bo + B1Ili + Ei;
-0.0026
• Model 2 Y; = Bo + B2r21 + €,
e.0275
-0.0626 0.0338
0.0140
-0.0568 -0.0737 -0.0521 -0.0505
-0.0370 -0.0160 -0.0234 -0.0266
• Model 3 Y; = Bo + B1ru + B2r2i + Ei
(a) What could you say about the significance of the parameters in the three models?
0.0575
0.0508 0. 0603 0.0548
0.0103
-0.0138 0.0237
-0.0017 0. 0038
-0.0403 -0.0326 -0.0304 -0.0259
0.0147
-0.0010
0.0069
(b) Are the data satisfying the normality assumption in each model?
(c) The adjusted R tells us which is the best model, when we have different number
of exogenous variables across the models. As for the R, the model with the
highest adjusted R2 is the best. By using the adjusted R2, state which is the best
model across Model 1, Model 2 and Model 3.
0.0054 0.0222
0.0303 0.0947
0.0142
0.0137
0.0295 0.0299
(d) For the best model, compute the predicted values when the new data are the X1
vector of values.
(e) Show the predicted values and the prediction interval (at 95% and at 90%) in a
plot.
(f) Are the predicted values far away from the real values of Y, for the 90% and 95%
case?
Transcribed Image Text:Consider a set of equity returns from four different markets across 12 different periods. The data are available in the marketdata.txt. Define the forth variable as your response variable (Y). Define the following three models: Mkt_1 0.0083 -0.0012 -0.0372 0.0090 -0.0549 -0.0521 -0.0462 -0.0567 Mkt 2 0.0427 Mkt_3 Mkt4 -0.0179 -0.0039 • Model 1 Y; = Bo + B1Ili + Ei; -0.0026 • Model 2 Y; = Bo + B2r21 + €, e.0275 -0.0626 0.0338 0.0140 -0.0568 -0.0737 -0.0521 -0.0505 -0.0370 -0.0160 -0.0234 -0.0266 • Model 3 Y; = Bo + B1ru + B2r2i + Ei (a) What could you say about the significance of the parameters in the three models? 0.0575 0.0508 0. 0603 0.0548 0.0103 -0.0138 0.0237 -0.0017 0. 0038 -0.0403 -0.0326 -0.0304 -0.0259 0.0147 -0.0010 0.0069 (b) Are the data satisfying the normality assumption in each model? (c) The adjusted R tells us which is the best model, when we have different number of exogenous variables across the models. As for the R, the model with the highest adjusted R2 is the best. By using the adjusted R2, state which is the best model across Model 1, Model 2 and Model 3. 0.0054 0.0222 0.0303 0.0947 0.0142 0.0137 0.0295 0.0299 (d) For the best model, compute the predicted values when the new data are the X1 vector of values. (e) Show the predicted values and the prediction interval (at 95% and at 90%) in a plot. (f) Are the predicted values far away from the real values of Y, for the 90% and 95% case?
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