Statistics for Business Assignment

This article discusses various aspects of Statistics for Business, including scatter plots, least squares linear equations, residual plots, and multiple regression models. It also provides examples and interpretations of these concepts. The article is aimed at students studying Statistics for Business and related courses.

Statistics for Business assignment
Student’s Name
Institution Affiliation

OECD Part 1
a. Description of the association in scatter plot of GDP and Trade balance
Below is the scatter diagram showing the relationship between the GDP and Trade
balance. The construction was done using Microsoft Excel software.
-15 -10 -5 0 5 10 15 20 25
0
10000
20000
30000
40000
50000
60000
70000
80000
f(x) = 1617.46876040526 x + 26804.1486268611
Scatter Plot for the GDP on Trade Balance
Trade Balance
GDP
The relationship in the scatter plot moves in the right direction. The correlation appears to be
linear as most data points are clustered along the trend line as shown in the above scatter plot.
b. Estimation of the least squares linear equation for the GDP on Trade balance.
The estimation was done on Microsoft Excel software. The following are the results obtained.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.70920
815
R Square 0.50297
62
Adjusted R
Square
0.48522
535
Standard
Error
11298.1
276
Observation
s
30
ANOVA
df SS MS F Significa
nce F
Regression 1 36169394
31
361693
9431
28.3353
3076
1.1472E-
05
Residual 28 35741352
35
127647
687
Total 29 71910746
67
Coeffici
ents
Standard
Error
t Stat P-value Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 26804.1
486
2135.855
465
12.5496
079
5.14181
E-13
22429.04
7
31179.2
502
22429.0
47
31179.2
502
Trade Bal
(%GDP)
1617.46
876
303.8587
579
5.32309
41
1.14722
E-05
995.0423
11
2239.89
521
995.042
311
2239.89
521
Therefore, the equation of the fitted line will be
GDP=26809.15+1617.47Trade balance
c. Interpretation of the Fitted linear equation
The fitted intercept is 26804.15 and the slope is 1617.47. The intercept value shows that the
GDP will be at 26809.15 when the trade balance is zero. The slope value implies that, when the
trade balance change by one unit the GDP will change( in the same direction ) by 1617.47.

d. Residual plot for the regression in section b above.
-15 -10 -5 0 5 10 15 20 25
-30000
-20000
-10000
0
10000
20000
30000
f(x) = − 1.81041929611722E-12 x + 8.15163625937601E-12
Trade Bal (%GDP) Residual Plot
Trade Bal (%GDP)
Residuals
The points in the residual plot do not form a regular pattern, therefore, the plot does not provide
a suitable summary for the residual variation of the regression model in section b above.
e. The country with the largest values of the two variables(GDP and Trade balance)
From the given data it’s observed that Australia is the country with the largest GDP of 70200 and
Trade balance of 21.6% GDP. This was not my expectation, I thought the USA could be the one.
f. Location of the USA on the scatter plot
The graph below shows the location of the USA on the scatter plot.

-15 -10 -5 0 5 10 15 20 25
0
10000
20000
30000
40000
50000
60000
70000
80000
4200
f(x) = 1617.46876040526 x + 26804.1486268611
Scatter Plot for the GDP on Trade Balance
Trade Balance
GDP
The point marked in red (-5.8, $ 4200), represent the USA.
The residual is given by observed results ($ 4200 for the USA) minus the predicted value
The predicted value will be computed using regression model;
GDP=26809.15+1617.47Trade balance
¿ GDP=26809.15+ 1617.47 ( −5.8 )
¿ $ 17427.8
Therefore the USA residual will be
Residual=4200−17427.8=−13222.8
This suggests that a bigger variation in GDP, the predicted GDP is higher than the observed
GDP.

OECD Part 2
a. Countries with balanced imports and exports and Average GDP Per cap
Here, the 95% confidence interval will be computed on SPSS software.
Coefficientsa
Model 95.0% Confidence Interval
for B
Lower Bound Upper Bound
1 (Constant) 22429.047 31179.250
TradeBalGDP 995.042 2239.895
a. Dependent Variable: GDPpercap
From the information in the table above the estimated range of average per capita GDP for
countries with imports and exports is ($ 22, 429.05, $ 31, 179.25)
a. Krokozia minister claim
The claim is plausible since the trade balance ranges between $ 995.04 and $ 2, 239.90.
b. 95% prediction interval when OECD uses the model in b above to predict a
balanced trade.
From the information in the table above, the 95% interval will be computed as follows

multiplier Upper limit Lower limit 95% Confidence Interval
Lower Upper
intercept 31179.250 22429.047 31179.250 22429.047
Trade
balance
1.02 2239.895 995.042 23,444 33,463.94
c.
The answer in a and c differ. They should differ due to the increase in the trade balance which
also affects the GDP.
The result in a and c differ from each other. They are supposed to differ due to the introduction
of a new change in the slope coefficient by the 2% increase.
OECD Part 3
b. Countries with balanced imports and exports and Average GDP Per cap
Here, the 95% confidence interval will be computed on SPSS software.
Coefficientsa
Model 95.0% Confidence Interval
for B
Lower Bound Upper Bound
1 (Constant) 22429.047 31179.250
TradeBalGDP 995.042 2239.895
a. Dependent Variable: GDPpercap

From the information in the table above the estimated range of average per capita GDP for
countries with imports and exports is ($ 22, 429.05, $ 31, 179.25)
c. Krokozia minister claim
The claim is plausible since the trade balance ranges between $ 995.04 and $ 2, 239.90.
d. 95% prediction interval when OECD uses the model in b above to predict a balanced
trade.
From the information in the table above, the 95% interval will be computed as follows
multiplier Upper limit Lower limit 95% Confidence Interval
Lower Upper
intercept 31179.250 22429.047 31179.250 22429.047
Trade
balance
1.02 2239.895 995.042 23,444 33,463.94
e.
The answer in a and c differ. They should differ due to the increase in the trade balance which
also affects the GDP.
The result in a and c differ from each other. They are supposed to differ due to the introduction
of a new change in the slope coefficient by the 2% increase.

OECD Part 4
a. Examing the scatter plot of response (GDP) versus explanatory variables (Trade
Balance and Mini Waste) and scatter plot between two explanatory variables.
The analyses were done using SPSS software.

From the third chart, it’s clear that the explanatory variables are not linearly associated. This
implies that there’s no multicollinearity in the regression model.
b. The partial slope for trade balance: Given that DP=$ 26,714+ $ 1.441 Trade Balance
No, the slope will not be the same, the coefficient will change if we use multiple regressions
there will be impact of both the variables on the regression model.
c. Fitting Multiple regression
Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence
Interval for B
B Std.
Error
Beta Lower
Bound
Upper
Bound
1
(Constant) -
4350.991
4938.051 -.881 .386 -
14483.035
5781.053
TradeBalGDP 1157.763 204.526 .508 5.661 .000 738.109 1577.416
MuniWastekgperson 61.843 9.428 .588 6.559 .000 42.498 81.188
a. Dependent Variable: GDPpercap
GDP=−4351+1157.8 Trade balance+61.8 Muni Waste
Comparing this model with the initial model the coefficient of trade balance has decreased to
1157.8
d. Conditions for the use of the MRM

ANOVAa
Model Sum of
Squares
df Mean Square F Sig.
1
Regression 5812961845.
314
2 2906480922.
657
56.944 .000b
Residual 1378112821.
352
27 51041215.60
6
Total 7191074666.
667
29
a. Dependent Variable: GDPpercap
b. Predictors: (Constant), MuniWastekgperson, TradeBalGDP
The model meets the MRM conditions, since its p-value, 0.00 is less than 0.05 significance level.
This shows that the model is statistically significant (Aiken,West &Ren,1991).
e. Path diagram for the estimated model
Trade Balance
(%GDP)
Muni Waste
(kg/person)
GDP per cap

f.
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95.0% Confidence
Interval for B
B Std.
Error
Beta Lower
Bound
Upper
Bound
1
(Constant) -
4350.991
4938.051 -.881 .386 -
14483.035
5781.053
TradeBalGDP 1157.763 204.526 .508 5.661 .000 738.109 1577.416
MuniWastekgperson 61.843 9.428 .588 6.559 .000 42.498 81.188
a. Dependent Variable: GDPpercap
From the table above the confidence interval can be summarized as follows.
GDP Trade Balance Mini Waste
Largest 70, 200 21.6 760
Smallest 4, 200 -8.6 260
95%
Confidence
Interval
Upper 1577.42 738.11
Lower 81.19 81.19

Reference
Aiken, L.S., West, S.G. and Reno, R.R., 1991. Multiple regression: Testing and interpreting
interactions. Sage