Suppose you have the following estimation results from the quarterly data of 195

Question

Suppose you have the following estimation results from the quarterly data of 1958 1st quarter to 1976 4th quarter: y_t - 2.40 + 0.103x_1 (3.4) (0.041) where the standard errors are in parentheses, Residual Sum of Squares (ESS)=18.48, and Total Sum of Squares (TSS)=128.08. Assume that Classical Assumptions for SLRM (Simple Linear Regression Model) hold. Do the following questions. Let beta be the population coefficient on x_t. Determine the sample size (note that you have the quarterly data of 1958 1st quarter to 1976 4th quarter). Calculate R_2. Test the significance of x_t (i.e. Test H_0: beta = 0 against H_1: beta ne 0) under 5 % level of significance. Test the significance of x_t (i.e. Test H_0: beta = 0 against H_1: beta ne 0) under 1 % level of significance. Test H_0: beta = 0.1 against H_1: beta ne 0.1. Compute a 99% confidence interval for beta.

Explanation / Answer

Result:

a).

sample size =76

b).

R square = (128.08-18.48)/128.08

=0.85571

c).

t = 0.103/0.041 =2.5122

df for error =74

Critical t at 5% level =1.993

Calculated t=2.5122 > critical value 1.993.

Ho is rejected.

Under 5% level ,it is significant.

d).

Critical t at 5% level =2.644

Calculated t=2.5122 < critical value 2.644.

Ho is not rejected.

Under 1% level ,it is not significant

e).

t=(0.103-0.1)/0.041 =0.0732

Calculated t=0.732 < critical value at 5% level 1.993.

Ho is not rejected.

f).

99% critical value of t with 74 df is 2.644

Lower limit of 99% CI for slope = 0.103-2.644*0.041 =-0.0054

upper limit of 99% CI for slope = 0.103+2.644*0.041 = 0.2114

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