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:

yt = 2.40 + 0.103xt

(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 ? be the population coefficient on xt.

(a) Determine the sample size (note that you have the quarterly data of 1958 1st quarter to 1976 4th quarter).

(b) Calculate R2.

(e) TestH0 :?=0.1againstH1 :??=0.1.

(f) Compute a 99% confidence interval for ?.

Explanation / Answer

Part (a)

Sample size: Q1 of 1958 to Q4 of 1976 gives 19 years or 76 quarters. Since the figures used for the regression analysis are quarterly figures, sample size is: 76 ANSWER

Part (b)

Given TSS = 128.08 and RSS = 18.48, the Regression SS = 128.08 – 18.48 = 109.60.

R2 = Regression SS/TSS

= 109.6/128.08

= 0.8557 ANSWER

Part (c)

To test = 0 = 0

t = (b - 0)/SE(b) tn – 2

Estimate of 2 is given by s2 = (Syy – b2Sxx)/(n - 2).

Standard Error of b is sb, where sb2 = s2/Sxx

t = (0.103 - 0)/0.041

= 103/41

= 2.512.

Upper 2.5% of t74 = 1.992

Since 2.512 > 1.992, the hypothesis = 0 = 0 is rejected. ANSWER

part (d)

upper 0.5% point of t74 = 2.664 which is greater than 2.512 and so the hypothesis = 0 = 0 is accepted. ANSWER

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