HI6007 Statistics: Business Decisions Assignment Solution Guide

This document presents a solved assignment related to Statistics for Business Decisions. It includes solutions to questions involving ANOVA and regression analysis, specifically focusing on interpreting statistical outputs and making informed business recommendations. The ANOVA section analyzes the mean output of four programs, advising Allied Corporation to select Program C due to its high mean output and low variance. The regression analysis section examines the relationship between a company's sales, competitor's prices, and advertising expenditures, determining the significance of each factor and re-estimating the regression equation after removing insignificant variables. The assignment concludes with an interpretation of the slope coefficient, highlighting the positive relationship between competitor's prices and the company's sales. The assignment uses data analysis and statistical techniques to provide actionable insights for business decision-making.

Statistics For Business Decisions
Statistics for Business Decision Assignment
Student’s Name
Institution Affiliation

Statistics For Business Decisions
Question Three
Data: Record of Outputs of Four Program test by Allied Corporation
Program A Program B Program C Program D
150 150 185 175
130 120 220 150
120 135 190 120
180 160 180 130
145 110 175 175
a. ANOVA Table test the difference between mean output of the four programs
It was constructed using Microsoft Excel.
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Program A 5 725 145 525
Program B 5 675 135 425
Program C 5 950 190 312.5
Program D 5 750 150 637.5
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 8750 3 2916.666667 6.14035
1
0.0055
7
3.23887
2
Within Groups 7600 16 475
Total 16350 19

Statistics For Business Decisions
b. Advice to Allied Corporation
P-value, 0.00557 is less than 0.05, implying that there's significant difference between mean
outputs of different Programs (Ruppert, 2014). These differences make the comparison of the
output of the four Programs simple and easier. Also, from table of summary, it clear that means
of output of the programs are different. Therefore Allied can select the program with higher
mean output which is associated with small Variance. Small Variance is an indicator of low
variation (risk) of the outputs. Allied should choose Program C, as its mean output is the highest
and has the smallest variance among the four programs
Question Four
Data: A company record of weekly Sales for its product (Y ) the unit price of the
competitor's product (X1), and advertising expenditures ( X2)
Week Sales of Product Y Price of Competitor Product
X1
Advertising Expenditures
X2
1 20 0.33 5
2 14 0.25 2
3 22 0.44 7
4 21 0.4 9
5 16 0.35 4
6 19 0.39 8
7 15 0.29 9

Statistics For Business Decisions
a. Regression Equation
Below is table showing the output of Regression Analysis
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8778
R Square 0.7706
Adjusted R Square 0.6558
Standard Error 1.8374
Observations 7
ANOVA
df SS MS F
Significa
nce F
Regression 2 45.3528
22.6
764
6.71
68 0.0526
Residual 4 13.5043
3.37
61
Total 6 58.8571
Coeffic
ients
Standard
Error
t
Stat
P-
valu
e
Lower
95%
Upper
95%
Lower
90.0%
Upper
90.0%
Intercept 3.598 4.052
0.88
8
0.42
5 -7.653 14.848 -5.041 12.236
Price of
Competitor Product
X1 41.320 13.337
3.09
8
0.03
6 4.290 78.350 12.887 69.753
Advertising
Expenditures X2 0.013 0.328
0.04
0
0.97
0 -0.896 0.923 -0.685 0.712
The estimated regression equation will be written as
Y =3.598+41.32 X1 +0.013 X2

Statistics For Business Decisions
b. Significance of the overall model presented in part a, at α=0.1 level.
The model is not statistically significant at 0.1, since its P-value 0.0526 is slightly higher than
0.05.
c. Significance of Competitor's Price and Advertising at 0.1 level
Competitor's Price (X1) is statistically significant, as it P-value, 0.0363 is less than 0.05. On the
other hands advertising ( X2) is insignificant since it P-value, 0.9697 is greater than 0.05.
d. Re-estimation of the Regression equation by getting rid of Advertising(X2),
insignificant Term in the first model, Y =3.598+ 41.32 X1 +0.013 X2
The table below, shows the result of regression Analysis between Sales for its product (Y ) and
Competitor's Price (X1)

Statistics For Business Decisions
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8778
R Square 0.7705
Adjusted R Square 0.7246
Standard Error 1.6438
Observations 7
ANOVA
df SS MS F
Significa
nce F
Regression 1 45.3473
45.3
473
16.7
831 0.0094
Residual 5 13.5098
2.70
20
Total 6 58.8571
Coeffic
ients
Standard
Error
t
Stat
P-
valu
e
Lower
95%
Upper
95%
Lower
90.0%
Upper
90.0%
Intercept 3.5818 3.6082
0.99
27
0.36
64 -5.6934
12.857
0 -3.6889 10.8525
Price of
Competitor
Product X1 41.603 10.1552
4.09
67
0.00
94 15.4982
67.707
9 21.1398 62.0663
The new regression Equation will be written as
Y =3.582+41.603 X1
e. Interpretation of slope coefficient

Statistics For Business Decisions
The slope coefficient is 41.603. This value is positive which indicate a positive gradient and
relationship between of product (Y ) and Competitor’s Price (X ¿ ¿1)¿(Francis,2004).This implies
that when Competitor’s price change by one unit, the Sale of product will change by 41.603
References
Francis, A. (2004). Business mathematics and statistics. Cengage Learning EMEA.
Ruppert, D. (2014). Statistics and finance: an introduction. Springer.