# Durbin Watson (d) Test

1(a) The Durbin Watson (d) statistic is defined as

(see attached)

Where u t is the OLS residual. Explain what hypothesis d tests.

(b) Show that if the null hypothesis is true, d is approximately equal to 2.

(c) The following equation was estimated by OLS on UK quarterly data

Ct = âˆ' 370.87 + 0.916YDt + u t t = 1,2,..,T
(218.0) (0.0047)

R2= 0.997, F = 37,986.0, d = 1.237, T = 111, standard errors in

brackets, u t is the least squares residual, Ct is expenditure on consumption goods and YDt is disposable income.
Calculate a 95% confidence interval for the coefficient of YDt.

(d) Give the assumptions on which your confidence interval in (c) is based. Is there any evidence given above that these assumptions are violated? Explain and discuss the implications, if any, for your confidence interval.

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The solution provides steps to determining validity of hypotheses and includes a graph in the word document.

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1(a) The Durbin Watson (d) statistic is defined as

2
Ë† Ë†
âˆ‘ (u t âˆ’ u t âˆ’1 )
d=
Ë†2
âˆ‘ut

Ë†
Where u t is the OLS residual. Explain what hypothesis d tests.

(b) Show that if the null hypothesis is true, d is approximately equal to 2.

(c) The following equation was estimated by OLS on UK quarterly data

Ë†
Ct = âˆ’ 370.87 + 0.916YDt + u t t = 1,2,..,T
(218.0) (0.0047)

R2= 0.997, F = 37,986.0, d = 1.237, T = 111, standard errors in
Ë†
brackets, u t is the least squares residual, Ct is expenditure on
consumption goods and YDt is disposable income.
Calculate a 95% confidence interval for the coefficient of YDt.

(d) Give the assumptions on which your confidence interval in (c) is
based. Is there any evidence given above that these assumptions are violated?
Explain and discuss the implications, if any, for your confidence interval.