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: FR=a+BOIL+YEXP+8FDI 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 MS F Regression 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values *, **', ?'and ??" d) Hence test whether B 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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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:
FR=a+B0IL+YEXP+8FDI
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
ЕXP
-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
MS
F
Regression
3
1991.31
663.77
?
??
Error
12
77.4
6.45
Total
15
a) What is dependent and independent variables?
b) Fully write out the regression equation
c) Fill in the missing values *', **', '?’and ??'
d) Hence test whether B 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a3f2e7d-5cb8-4afa-9389-12614fdb6539%2F20e89849-122b-46e5-95de-f7ff05e1712d%2Fd5tocug_processed.jpeg&w=3840&q=75)
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