Topic: Coursework for Empirical Finance

  •  

Bill, an undergraduate student in Accounting and Finance, is examining the relationship between innovation and firm size in the chemical industry. The following simple regression was estimated

using the data on 28 companies:

Where variable rd denotes annual expenditures on research and development (R&D), and sales denotes annual sales, both are in millions of dollars.  is the dependent variable y, and is the independent variable x. The disturbance terms, , are assumed to be normally and independently distributed with a mean of zero and constant variance s2.  He has completed a preliminary analysis of the sample data and produced the following sample information:

Lower case letters indicate that the variables are measured as deviations from their respective sample means i.e = .

Use the above sample information to answer all following questions. Show allcalculations explicitly.

  1. Calculate estimates, b0 and b1, for the unknown equation coefficients,  and .

[10 marks]

  • Write down the regression equation and interpret the estimated coefficients.

[5 marks]

  • Calculate the estimated standard errors of the estimated coefficients.

[5 marks]

  • Perform a test of the null hypothesis H0:  = 0 against the alternative hypothesis.

[5 marks]

  • Compute the value of R2 for the estimated regression. Briefly interpret the meaning of R2.

 [5 marks]

[Total 30 marks]

  •  
    • Define the four assumptions that need to hold under the Gauss-Markov Theorem(include the relevant mathematical expressions in your answer).

[10 marks]

  • What is the main contribution of the Gauss-Markov Theorem to modelling?

 [5 marks]

 [Total 15 marks]

  •  
    • Explain the problem of heteroskedasticity.

                                                                                                                           [5marks]

  • What are the consequences of heteroskedasticity for OLS?      

                                                                                                                           [5marks]

  • How the presence of heteroskedasticity can be tested?

                                                            [5 marks]

 [Total 15 marks]

Q4.

6.1The linear regression model below is estimated to analyse the demand for petrol in the UK (ct),

     disposable income (yt) and the price index of petrol (pt) are included as explanatory variables. The

data contain 43 observations from 1968 to 2010.

. reg c y p   Source |       SS           df       MS      Number of obs   =        43 ————-+———————————-   F(2, 40)        =    175.66 Model |  .879902606         2  .439951303   Prob> F        =    0.0000 Residual |  .100181351        40  .002504534   R-squared       =    0.8978 ————-+———————————-   Adj R-squared   =    0.8927 Total |  .980083958        42  .023335332   Root MSE        =    .05005   —————————————————————————— c |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval] ————-+—————————————————————- y |    .731198   .0765292     9.55   0.000     .5765268    .8858692 p |  -.1007774    .034183    -2.95   0.005    -.1698637    -.031691 _cons |  -18.91766   .6265087   -30.20   0.000    -20.18388   -17.65144       dwstat // Durbin-Watson test   Durbin-Watson d-statistic(  3,    43) =  .1266305
  1. The residuals of the regression are plotted in the figure below. The pattern of residuals implies that the assumptions for simple linear regression might not be satisfied. Discuss the potential problem.

[10marks]

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b)    Suppose the errors in the above case follow the AR(1) model. For instance, we assume that

Perform a Durbin-Watson test (at both 5% and 1% significant levels) and interpret the results.

[10 marks]

Type of service-Academic paper writing
Type of assignment-Coursework
Subject-Statistics
Pages / words-11 / 3000
Number of sources-5
Academic level-Undergraduate
Paper format-Harvard
Line spacing-Double
Language style-UK English

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