# 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 = − 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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#### Solution Preview

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

d = sum of (u-hat_t - u-hat_t-1)^2/ sum of u-hat (2 -- t)

where u-hat_t is the OLS residual. Explain what hypothesis d tests.

Solution: The Durbin-Watson statistic d is used to test for the presence of autocorrelation in the residuals of a regression equation. The test compares the residual for time period t with the residual from time period t-1 and develops a statistic that measures the significance of the correlation between these successive comparisons. The statistic d has a range from 0 to 4 with a midpoint of 2 and can be used to test for the presence of both positive and negative correlation in the residuals.

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

Solution: The null hypothesis for Durbin-Watson statistic is given as:

H0: There is no significant correlation

The Durbin-Watson statistic is approximately equal to 2*(1-R), where R equals the ...

#### Solution Summary

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