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1 The following regression is estimated with T=22 observations: Yt = B1 + B2x2t + B3X3+ + ut The regression output reported TSS = 15
1 The following regression is estimated with T=22 observations: Yt = B1 + B2x2t + B3X3+ + ut The regression output reported TSS = 15.0, ESS = 10.0 and RSS = 5.0, where TSS is the total sum of squares, ESS is the explained sum of squares and RSS is the residual sum of squares from the regression. The F-statistic for the test of overall significance of the regression is equal to: Select one: O A. 3.33 O B. None of these O C. 5 O D. 20 E. 10
2
A simple regression model is estimated, and the following results are obtained: R2 = 0.87 y = 0.8 +1.6x, [1.5] [6.4] where t-statistics are shown in square brackets. The null hypothesis is that the true coefficient on X2, is equal to one (i.e. B=1). The test statistic for this null hypothesis is: Select one: A. 6.4 B. 0.5333 C. 0.0938 D. 3.2 O E. 2.4
Expert Solution
1 The F statistic is used to test the overall significance of a test.
F=(ESS/df)/ (RSS/df)
where df is the degrees of freedom associated with ESS and RSS.
now df for ESS is (K-1) and df for RSS is (n-k), where k is the number of parameters to be estimated in the regression model and N is the total nimber of observations.
In the given sum, n=22 and k=3
So, F= (10/3-1)/(5/22-3)
F= (10/2)/(5/19)
F=5/0.26
F=19.23
SInce, 19.23 is not given in the options the answer is B. NONE OF THESE.
2
The test statistic is a t-statistic. It is defined by the following equation.
t = (b - β ) / SE
Where b is the coefficient of X2t or slope of the simple regression model.
SE is the standard error.
Null hypothesis : β = 1
---------------
t = (b - β) / SE
=> t = (1.6 -1 )/ 6.4
=> t = 0.6 / 6.4
=> t = 0.09375
=> t = 0.0938
The test statistic of this null hypothesis is 0.0938
Answer: Option (C)
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