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