Introductory Econometrics

Note Yall = All 50 observations on Y;
Xall = All 50 observations on X.
Questions:
(a) Test (i) at 10%% level of significance and (ii) at 5% level of significance the hypothesis that the model has changed in the way the researcher has specified. Detail all procedure and show all calculations. (18 marks)
(b) Use the regression output to draw the two fitted lines (before and after) on the same set of axes.
[Note: You do not need to use a graph paper, nor do you have to draw these lines to scale but you need to label all axes, indicate the gradient of each line and mark all intercepts correctly] (7 marks)

Introductory Econometrics

Task 1:?
Consider the Classical Linear Regression Model?
Y = a + ßX + e?
Here Y = Price and X = mpg (miles per gallon) of a car.
The model is estimated (as given by the Stata regression output below) using data on 74 observations. However, parts of the regression output, denoted by the query mark (?), are missing.

.    (a) Use the available information to calculate the missing numbers. Show all workings. (13 marks) ?
.    (b) Explain how the 95% confidence interval for the constant coefficient was calculated. (5 marks) ?
.    (c) Test the hypothesis that x has an effect on Y. What is the p-value of your test? (7 marks) ?
.
Task 2:
Suppose that a researcher suspects that an underlying relationship between a dependent variable Y and an independent variable X has changed due to an economic shock as follows:
Classical Linear Regression Model (CLRM) before:
Y = ß1 + ß2X + e
Classical Linear Regression Model (CLRM) after:
Y = ß1’ + ß2X + e
In order to test this hypothesis the researcher proposes a dummy augmented model as follows:
Y = ß1 + ß2X +( ß1’ – ß1)*Dummy + e
The variable Dummy is defined as follows:
Dummy = 0 for the data before the shock
Dummy = 1 for the data before the shock
The researcher pools 20 observations from the period before the shock and 30 from the period after and runs an OLS regression. The Stata output is presented below:

Note Yall = All 50 observations on Y;
Xall = All 50 observations on X.
Questions:
(a) Test (i) at 10%% level of significance and (ii) at 5% level of significance the hypothesis that the model has changed in the way the researcher has specified. Detail all procedure and show all calculations. (18 marks)
(b) Use the regression output to draw the two fitted lines (before and after) on the same set of axes.
[Note: You do not need to use a graph paper, nor do you have to draw these lines to scale but you need to label all axes, indicate the gradient of each line and mark all intercepts correctly] (7 marks)

Introductory Econometrics

Task 1:?
Consider the Classical Linear Regression Model?
Y = a + ßX + e?
Here Y = Price and X = mpg (miles per gallon) of a car.
The model is estimated (as given by the Stata regression output below) using data on 74 observations. However, parts of the regression output, denoted by the query mark (?), are missing.

.    (a) Use the available information to calculate the missing numbers. Show all workings. (13 marks) ?
.    (b) Explain how the 95% confidence interval for the constant coefficient was calculated. (5 marks) ?
.    (c) Test the hypothesis that x has an effect on Y. What is the p-value of your test? (7 marks) ?
.
Task 2:
Suppose that a researcher suspects that an underlying relationship between a dependent variable Y and an independent variable X has changed due to an economic shock as follows:
Classical Linear Regression Model (CLRM) before:
Y = ß1 + ß2X + e
Classical Linear Regression Model (CLRM) after:
Y = ß1’ + ß2X + e
In order to test this hypothesis the researcher proposes a dummy augmented model as follows:
Y = ß1 + ß2X +( ß1’ – ß1)*Dummy + e
The variable Dummy is defined as follows:
Dummy = 0 for the data before the shock
Dummy = 1 for the data before the shock
The researcher pools 20 observations from the period before the shock and 30 from the period after and runs an OLS regression. The Stata output is presented below:

Note Yall = All 50 observations on Y;
Xall = All 50 observations on X.
Questions:
(a) Test (i) at 10%% level of significance and (ii) at 5% level of significance the hypothesis that the model has changed in the way the researcher has specified. Detail all procedure and show all calculations. (18 marks)
(b) Use the regression output to draw the two fitted lines (before and after) on the same set of axes.
[Note: You do not need to use a graph paper, nor do you have to draw these lines to scale but you need to label all axes, indicate the gradient of each line and mark all intercepts correctly] (7 marks)