This is the needed information to answer those questions. Many thanks! An accoun

Question

This is the needed information to answer those questions. Many thanks!

An accountant is interested in how the level of inventories (l) is related to the cost of borrowing (R) and sales (S). She formulates the following model: I_i = beta_0 + beta_1 S_i + beta_2 R_i + u_i For a sample of 35 firms in the same industry sector she obtains the OLS results Regn1 in the table below. A colleague suggests that she also test for heteroskedasticity as sales may be correlated across firms in the industry. She sorts the variables appropriately and regresses the top and bottom 14 firms producing Regns 2 and 3 respectively, then Regn 4 is the result if heteroskedasticity is to be accounted for. (t-values are in parentheses and ESS is the error sum of squares) Perform a test against heteroskedasticity stating clearly the null hypothesis, the distribution of the test statistic and the rejection rule. What criteria would you expect the accountant to have used to sort the variables? From your answer in (a) explain conceptually, how Regn1 and Regn4 differ? State clearly how the constants and slope coefficients are calculated.

Explanation / Answer

a)

Null Hypothesis:The variances of the error are constant.

Alternative Hypothesis:The variances of the error are not constant.

Significance level =0.05

Statistical test:Goldfeld Quandt test

Rejection Rule:Reject Ho if F>Fcritical

The F-value is the ratio of ESS2/ESS1 which is in this case = 5.114/.908 = 5.632

As the F-value is large than the critical F-value of 2.82(F(11,11)) therefore we will reject the null hypothesis and conclude that the variances are not equal.

b)The above statistical test is to test the homoscedasticity using Goldfeld-Quant test .It is based on the arrangement of data in ascendening order and then dividing the observation into three part with upper and lower value being equal.

c)As there is heteroscedasticity there fore Regn4 is accounted.As the variances of errors within are not constant therefore the error term will be in a funnel shaped making the two regression variances of error being different.(Regn1 and Regn4).The constants and slopes are calculated from the obsevation of cost of borrowing(R) amd sales(S) using multiple regression analysis using any statistical software package for the given observation under each Regn.

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