A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor           Coef              StDev          t-ratio        p-value Constant         5491.38          2508.81       2.1888       0.0491 OIL                  85.39             18.46            4.626         0.0006 EXP                 -377.08          112.19           *               0.0057 FDI                  -396.99          160.66         -2.471            ** S = 2.45  R-sq = 96.3%  R-sq(adj) = 95.3% Analysis of Variance Source        DF           SS            MS           F          p Regression    3        1991.31    663.77        ?          ?? Error             12        77.4          6.45 Total             15 d) Hence test whether ? is significant. Give reasons for your answer.  e) Perform the F Test making sure to state the null and alternative hypothesis.  f) Given an interpretation of the term “R-sq” and comment on its value.

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A researcher interested in explaining the level of foreign reserves for the country of Barbados
estimated the following multiple regression model using yearly data spanning the period 2001 to
2016:
??=?+????+????+????
Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports
($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed
using MINITAB and the following is an extract of the output obtained:


Predictor           Coef              StDev          t-ratio        p-value
Constant         5491.38          2508.81       2.1888       0.0491
OIL                  85.39             18.46            4.626         0.0006
EXP                 -377.08          112.19           *               0.0057
FDI                  -396.99          160.66         -2.471            **


S = 2.45  R-sq = 96.3%  R-sq(adj) = 95.3%


Analysis of Variance
Source        DF           SS            MS           F          p
Regression    3        1991.31    663.77        ?          ??
Error             12        77.4          6.45
Total             15

d) Hence test whether ? is significant. Give reasons for your answer. 
e) Perform the F Test making sure to state the null and alternative hypothesis. 
f) Given an interpretation of the term “R-sq” and comment on its value. 

 

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