Question

An attempt was made to evaluate the forward rate as a predictor of the spot rate in the treasury bill market. For a smaple of 122 quarterly observations, the estimated linear regression (standard error in parentheses)

S= -.002 + 0.8916F

(.1759)

was obtained where:

S=actual change in spot rate

F= change in spot rate predicted by the foward rate.

Test, against a two-sided alternative, the null hypothesis that the slop of the population regression line is 1.0.

i. State the null and alternative hypothesis

ii. State the decision rule to be employed if the level of significance is 1 percent.

iii. Calculate the value of the test statistic.

iv. Make the statistical decision.

v. Explain your decision in the context of the problem.

Answer 1

1. If the slope of the pupulation regression function is B say. Then we will have the hypothesis structured as H0: B=1, H1: B not equal to 1. This would then be a 2 sided test. H0 is the null hypothesis and H1 the alternative hypothesis.

2. In case the level of significance is 1% the after conducting the t test for the significance of B we will reject the null hypothesis if the p value is less than 0.01. We accept the null hypothesis otherwise.

3. The value of the t statistic is t =(0.8916-1)/(0.1759) = 0.62. Thus as the value of the t stat is less than 2 we accept the null hypothesis. The value of the slope coefficient is thus not significantly different from one.

4. We accept the null hypothesis.The value of the slope coefficient is thus not significantly different from one.