C7D1 - HETEROSCEDASTICITY 1 X X 3 X 5 X 4 X 1 X 2 Y = 1 + 2...

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Unformatted text preview: HETEROSCEDASTICITY 1 X X 3 X 5 X 4 X 1 X 2 Y = 1 + 2 X Y 1 This sequence relates to Assumption A.4 of the regression model assumptions and introduces the topic of heteroscedasticity. This relates to the distribution of the disturbance term in a regression model. HETEROSCEDASTICITY 1 X Y = 1 + 2 X Y 2 We will discuss it in the context of the regression model Y = 1 + 2 X + u . To keep the diagram uncluttered, we will suppose that we have a sample of only five observations, the X values of which are as shown. X 3 X 5 X 4 X 1 X 2 HETEROSCEDASTICITY 1 X Y = 1 + 2 X Y 3 If there were no disturbance term in the model, the observations would lie on the line as shown. X 3 X 5 X 4 X 1 X 2 HETEROSCEDASTICITY 1 X Y = 1 + 2 X Y 4 Now we take account of the effect of the disturbance term. It will displace each observation in the vertical dimension, since it modifies the value of Y without affecting X . X 3 X 5 X 4 X 1 X 2 HETEROSCEDASTICITY 1 X Y = 1 + 2 X Y 5 The disturbance term in each observation is hypothesized to be drawn randomly from a given distribution. In the diagram, three assumptions are being made. X 3 X 5 X 4 X 1 X 2 HETEROSCEDASTICITY 1 X Y = 1 + 2 X Y 6 One is that the expected value of u in each observation is 0 (Assumption A.3). The second is that the distribution in each observation is normal (Assumption A.6). We are not concerned with either of these and we will assume them to be true....
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C7D1 - HETEROSCEDASTICITY 1 X X 3 X 5 X 4 X 1 X 2 Y = 1 + 2...

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