Statistics of Business Studies: Regression Analysis and ANOVA Table

This article covers topics like constructing frequency distribution, histogram, regression analysis, ANOVA table and more in Statistics of Business Studies. It also provides expert guidance and advice for business decisions.

University
Statistics of Business Studies
By
Your Name
Lecturer’s Name
Date
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Question 1
Information about the examination score is provided in the form of a dataset and it is required of
us to construct a frequency distribution for the data and its histogram and describe the shape of
the distribution.
Solution
a. The frequency distribution table with the required columns is as shown in the excel file
and a replica of the same is as shown below:
b. The histogram showing the percent frequency distribution of the examination score is as
shown in the figure below:
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From observations of the above histogram we can conclude that the distribution of the
examination scores is positively skewed. This means that majority of the exam score lie
above the mean score thereby pulling the distribution to the right.
Question 2
A portion of computer output for regression analysis that shows the relationship that exist
between sales and unit price in thousands of dollars is provided as below and is to be used to
answer a series of set problems:
Solutions
a. The sample size for the problem is determined using the degrees of freedom for treatment
(DFT) and degree of freedom from the error (DFE).
DFT =K −1
Where DFT is the degree of freedom for treatment. Hence,
K−1=1 thus, K=2
The degree of freedom from the error is given by:
DFE=N−K
Therefore, solving for N we get the sample size is 41 as below:
39=N −2 thus , N =41
b. The least square regression equation from the table provided can be evaluated as:
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Y =0.029 X +54.076
Where Y is the dependent variable (supply) and the x represents the explanatory variable
(Unit price). The regression equation indicates there is a positive linear relationship
between sales and unit price. That is the sales increase with increase in unit price and
drop when the unit price drops.
c. The coefficient of determination is the r-squared value and is calculated using the
equation below:
R2= SSM
SST
The value of SST is the sum of squares for total while the value SSM represents the sum
of squares for the evaluated model. From the table provided SSM is 354.689 while the
SST value is (354.689+ 7035.262 =7389.951). The value of coefficient for determination
will therefore be given by:
R2= 354.689
7389.951 =0.047996
The coefficient of determination indicates the possibility of future sales and unit prices
being related in the same manner as in the regression equation above. The probability of
future supply and unit prices in this case of being related in the same manner is 0.047996.
d. The coefficient of correlation is the square root of the coefficient of determination as
shown below:
R= √ R2
In this case it will be:
√ 0.047996=0.219
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The coefficient of correlation indicates the direction and strength of the linear
relationship between the variables. In this case there is a weak positive linear relationship
between the value of supply and unit price.
e. To predict the value of supply when the value of unit price is $50000 dollars we use the
regression equation as below:
Y =0.029 X +54.076
Substituting x with the unit price provided because it is the independent variable, we get:
Y =0.029 (50000 )+54.076=1504.08 dollars
Hence the supply would be $1504.08 dollars when the unit supply was $50000.
Question 3
The data for the four programs that Allied corporation is intending to use to increase the
productivity of its line of workers is provided. The data is to be used to create an ANOVA table
and the resulting table used to provide advice to the corporation.
Solution
a. The ANOVA table constructed is as shown in the diagram below:
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b. The ANOVA table is used for hypothesis testing of the difference in means. If suppose,
the null hypothesis was that there is no difference in mean while the alternate hypothesis
is that there is difference in mean, the ANOVA table could be used to justify the claim
(Croucher, 2016). The null hypothesis is accepted if F<Fcrit and rejected otherwise. For the
case of the Allied Corporation F>Fcrit (6.14>3.24) thus we reject the null hypothesis as
there is sufficient evidence that there is a difference in the means. The Allied corporation
can therefore be advice not to carry on with the program since the programs will not
increase the productivity as expected.
Question 4
Information in the form of a dataset is provided for the weekly sales of products, the unit price of
the competitor’s product and the advertising expenditure is provided for a certain company. The
data is to be used for regression analysis.
Solutions
a. The regression output table developed is as shown in the diagram below:
The estimated regression equation is:
Y =41.32 X1+ 0.01 X2+ 3.60
Y is the sales, X1 is the unit price and X2 is the cost of advertising.
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b. A model is said to be statistically significant when the value of the significance F is less
the significance level of the whole model (Selvanathan, Selvanathan, and Keller, 2017).
In this case the significance F from the table in the excel sheet is 0.05 while the
significance level is 0.1. Since the significance F is less than the overall significance level
of the whole model, then the model can be said to be statistically significant.
c. To determine whether the competitors price and advertising are individually significantly
related to sales we look at their coefficients and p-values. The coefficient of competitor’s
price is 41.32 and the P-value is 0.04. The coefficient of advertising is 0.01 and its p-
value 0.97. The positive coefficient indicates a positive linear relationship of the variables
with sales. On the other hand, p-values less than overall significance level indicate that
there is significant relationship, however, the p value of advertising approaches 1
meaning that it has little impact on sales and can be presumed to be insignificant.
d. After dropping the insignificant variable which is advertising, the new model is as
follows:
the new regression equation can be estimated to be:
Y =41.60 X1 +3.6
e. The slope of the new model is 41.6 and it show the extent to which the significant
independent variable (Unit price) impacts the sales. That is, the value of unit price
impacts the value of sales by a factor of 41.6.
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References
Croucher, J. S. (2016). Introductory mathematics & statistics. 6th ed. Australia: North Ryde,
N.S.W. McGraw-Hill Education.
Selvanathan, E. A., Selvanathan, S., and Keller, G. (2017). Business statistics abridged. 7th ed.
South Melbourne, Victoria: Cengage Learning.
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