Introduction to Econometrics

Introduction to Econometrics

Question 1

x

y

xy

x^2

y^2

425

347.4

147645

180625

120686.8

402.8

352.2

141866.2

162247.8

124044.8

404.2

350.8

141793.4

163377.6

123060.6

401.8

309.6

124397.3

161443.2

95852.16

403.6

321.6

129797.8

162893

103426.6

419.1

329.1

137925.8

175644.8

108306.8

402

313.7

126107.4

161604

98407.69

383.5

289.6

111061.6

147072.3

83868.16

378.6

285.6

108128.2

143338

81567.36

401.8

284.8

114432.6

161443.2

81111.04

405.2

293.8

119047.8

164187

86318.44

 

 

 

 

 

Sum

4427.6

3478.2

1402203

1783876

1106650



r =

r = 0.639

The correlation coefficient between the variables shows that there exist a 63.9% relationship between the Tesco and Sainsbury's shares i.e. both the variables are explaining almost 64% relationship with each other. The relationship between the share prices is also positive showing that if one variable increases, then the other variable will also increases and 'r' shows that at which rate these variables are increasing and from the above results we can conclude that at a rate of 64%, both the variables are increasing.

It would not be feasible to estimate the regression analysis for these two variables and there exist a major reason for it. The main reason is that the r - square is not significantly high so that we can say that the significant relationship exists between the variables.

Question 2

Derivation of

The equation for OLS can be written as:

Where and are dependent variable and independent variable respectively. In the above equation, is the disturbance termare coefficients. The OLS procedure minimizes the error sum of squares (SSE). The following is the way through which its coefficients can be found out:



Now,

by dividing equation (i) by (ii)

by re-arranging the terms by dividing both the sides by n. by re-arranging again

by solving the OLS estimate

For finding we will solve in the following way:

(2)

(3)

Now multiplying the above equation by the sum of and equation (3) by n. Similarly, (4)

(5)

Subtract equation (4) from equation (5), we get:

(6)

Solving equation (6) yields the OLS estimate we get:

(7)

The estimated OLS regression equation can be written as:

Now, the major aim of the OLS estimator is to minimize the SSE of the equation so that we can reach the best estimated results that are close to the given data points. For this purpose we'll use the first order condition and differentiate the above equation with respect to the parameters. The reason of differentiating with respect to the parameters is that to find out the optimum value of the parameters that can minimize the SSE.

After differentiating the equation, we simplify the resulting equation and find out the value of in terms of. Then putting this value of back in the main equation and simplifying, we get the resulting values of and. It has to be noticed that the values are not the actual values but they are estimated showing best possible ...