Holmes Institute HI6007 - Statistics for Business Decisions Assignment

This assignment provides solutions to statistical problems relevant to business decisions. It includes constructing frequency distributions, analyzing regression outputs, performing ANOVA tests, and interpreting correlation coefficients. Specifically, it covers creating frequency, cumulative frequency, relative frequency, and percent frequency distributions from examination scores. It also analyzes the relationship between supply and unit price using regression analysis, including determining the sample size, significance, coefficient of determination, and predicted supply. Furthermore, it conducts an ANOVA test to compare the productivity of different programs and identifies the most productive one. Finally, it estimates and interprets regression equations to understand the impact of unit price and advertising on sales, determining the significance of the model and individual variables. Desklib provides this assignment as a resource for students, offering additional solved assignments and past papers.

Running Head: STATISTICS FOR BUSINESS DECISIONS
Statistics For Business Decisions
Name of the Student
Name of the University
Student ID

1STATISTICS FOR BUSINESS DECISIONS
Table of Contents
Answer 1....................................................................................................................................2
Answer 2....................................................................................................................................2
Answer 3....................................................................................................................................3
Answer 4....................................................................................................................................3

2STATISTICS FOR BUSINESS DECISIONS
Answer 1
(a)
Examination Scores Freq Cum. Freq Rel. Freq Cum. Rel. Freq Percent Frequency
50 - 60 3 3 0.15 0.15 15
60 - 70 2 5 0.1 0.25 10
70 - 80 5 10 0.25 0.5 25
80 - 90 4 14 0.2 0.7 20
90 - 100 6 20 0.3 1 30
Grand Total 20 1 100
(b) The figure shows that more students have secured higher marks. There is
mostly increase in the percentage of students with the increase in the examination
scores.
50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
0
5
10
15
20
25
30
Histogram Showing Percent Frequency Distribution
Scores
Percent Frequency
Answer 2
(a) The sample size for this problem is (Total df + 1) = (39 + 1 + 1) = 41.
(b) At 0.05 level of significance, it can be seen that the value of F is less than the critical
value of F. Thus, there is strong evidence to conclude that demand and unit price are
related.

3STATISTICS FOR BUSINESS DECISIONS
(c) The coefficient of determination (R2) has been obtained with the help of the following
formula:
R2=1−∑ of Squares of Residuals
Total ∑ of Squares =1− 7035.262
( 354.689+7035.262 ) =0.05
This indicates explanation of 5% variability in the demand by the unit price of the
product.
(d) The coefficient of correlation (R) can be evaluated with the help of the following
formula:
R= √ R2= √ 0.05=0.219
The correlation coefficient indicates a positive relationship between supply and unit
price. Increase in unit price will result in increasing supply.
(e) Predicted supply = 54.076 + (0.029 * 50) = 55.53 units ~ 56 units.
Answer 3
(a)
ANOVA
Sources SS df MS F P value F crit
Between Groups 7654.688 3 2551.563 5.319218 0.014567 3.490295
Within Groups 5756.25 12 479.6875
Total 13410.94 15 894.0625
(b) It can be seen that the P-value is less than 0.05, which indicates that there are
significant differences in the productivity of the different products. Program C has
shown the highest productivity. Thus, Allied needs to adopt Program C.
Answer 4
(a) The estimated Regression equation is
Sales (y) = 3.60 + (41.32 * Unit Price (x1)) + (0.01 * Advertisement (x2))

4STATISTICS FOR BUSINESS DECISIONS
REGRESSION OUTPUT
Regression Statistics
Multiple R 0.88
R Square 0.77
Adjusted R Square 0.66
Standard Error 1.84
Observations 7
ANOVA
df SS MS F
Significance
F
Regression 2 45.353 22.676 6.717 0.053
Residual 4 13.504 3.376
Total 6 58.857
Coefficient
s
Standard
Error t Stat
P-
value Lower 90%
Upper
90%
Intercept 3.60 4.052 0.888 0.425 -5.041 12.236
Price 41.32 13.337 3.098 0.036 12.887 69.753
Advertising 0.01 0.328 0.040 0.970 -0.685 0.712
(b) The significance F value from the ANOVA table is 0.053, which is less than 0.10.
Thus, the model is significant overall.
(c) The p-value for unit price is less than 0.10, and thus unit price is significantly related
to sales but the P-value for advertisement is more than 0.10, and thus advertisement is
not significantly related to sales.
(d) The re-estimated regression equation is given by:
Sales (y) = 3.58 + (41.60 * Unit Price (x1))
REGRESSION OUTPUT
Regression Statistics
Multiple R 0.88
R Square 0.77
Adjusted R
Square 0.72
Standard Error 1.64
Observations 7

5STATISTICS FOR BUSINESS DECISIONS
ANOVA
df SS MS F Significance F
Regression 1 45.347
45.34
7 16.783 0.009
Residual 5 13.510 2.702
Total 6 58.857
Coefficient
s
Standard
Error t Stat
P-
value
Lower
90.0%
Upper
90.0%
Intercept 3.58 3.608 0.993 0.366 -3.689 10.853
Price 41.60 10.155 4.097 0.009 21.140 62.066
(e) It can be said from the re-estimated regression equation that with each unit increase in
the unit price of the product, the sales of the product increases by 41.60 units.