Statistics: ANOVA, Regression Analysis and Hypothesis Testing

This article covers ANOVA, Regression Analysis and Hypothesis Testing in Statistics. It includes computation of sample size, hypothesis test, coefficient of determination, coefficient of correlation, regression model and significance of variables.

STATISTICS
Student Name
[Pick the date]

Question 1
(a) The relevant frequency distribution table is highlighted below.
(b) Histogram for percentage frequency distribution of score is highlighted below.
It is apparent from the above histogram that the distribution is non-normal with a negative skew
(Hillier, 2016). Also, the curve does not assume a bell shaped curve. Besides, the deviation in the
data seems to be quite high.
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Question 2
Dependent variable: supply (y) and
Independent variable unit price (x)
ANOVA table
(a) Computation of sample size
Degree of freedom (Dof) = 1+39 = 40
Sample size = 1+ Degree of freedom = 41
(b) Hypothesis test
H0: β=0
H1 : β ≠ 0
Slope coefficient b= 0.029
Corresponding standard error S Eb= 0.021
t stat= b−β
S Eb
=( 0.029−0.00
0.021 )=1.381
Dof = n-2 =41-2 = 39
The p value (two tailed test) ¿ TDIST (1.38 , 39,2)=0.175
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Level of significance α = 0.05
The p value > Level of significance
Therefore, sufficient evidence is not present for the rejection of null hypothesis (Hair, et. al.,
2015). Thus, it can be said that unit prices and supply is not statistically related.
(c) Computation of coefficient of determination R2
From ANOVA table
SSR=354.689 , SSE=7035.262
SST =(354.689)+(7035.262)=7389.9 5
R2= 354.68
7389.95 =0.04 8
The value of coefficient of determination represents that only 4.8% of changes in supply would
be described by change in unit prices. Further, the linear regression model would not be
considered as good fit as the value is close to zero (Hillier, 2016).
(d) Coefficient of correlation
R= √coefficient of determination2= √0.048
R=±0.21 9
The correlation coefficient would be positive as the sign of slope is positive. Therefore, the
coefficient would be +0.219. The value is low (lesser than 0.5) and hence, the strength of
correlation would be weak.
(e) Supply =?
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Unit price X = $50,000.
Regression equation
y (' 000)=54.076+0.029 x=54.076+ ( 0.029∗50 ) =55.526
Therefore, the total supply would be 55526 units for a unit price of $50,000.
Question 3
Four programs and their respective outputs is highlighted below.
(a) ANOVA table
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(b) Hypothesis
Null hypothesis H0: All the four group means are equal.
Alternative hypothesis H1: At least one group mean is not same.
The value of F (test statistic) comes out to be 6.14.
Level of significance = 0.05
The corresponding p value with respect to the test statistic comes out to be 0.006 which is lower
than the level of significance. Hence, sufficient evidence is present to reject the null hypothesis
and to accept the alternative hypothesis (Hillier, 2016). Therefore, the conclusion can be drawn
that one of group mean is not same.
Question 4
The weekly sales data fir its product is represented below.
(a) Regression model
Dependent variable = Sales
Independent variables = Price, advertising
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Regression equation
Sales=3.598+ ( 41.32∗Price ) +(0.013∗Advertising)
(b) Whether the model is significant or not.
Null hypothesis H0: Model is statistically insignificant.
Alternative hypothesis H1: Model is statistically significant.
Level of significance = 0.10
The value of significance F comes out to be 0.0526 which is lower than the level of significance
and therefore, null hypothesis would be rejected and alternative would be accepted (Flick, 2015).
The conclusion can be made that regression model is statistically significant.
(c) Whether the competitors’ price and advertising is significant to sales or not.
 Whether the competitors’ price is significant to sales or not.
Null hypothesis H0: Price is insignificant to sales.
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Alternative hypothesis H1: Price is significant to sales.
Level of significance = 0.10
The p value for price comes out to be 0.036 which is lower than the level of significance and
therefore, null hypothesis would be rejected and alternative would be accepted (Harmon, 2016).
The conclusion can be made that price is statistically significant to sales.
 Whether the advertising is significant to sales or not.
Null hypothesis H0: Advertising is insignificant to sales
Alternative hypothesis H1: Advertising is significant to sales.
Level of significance = 0.10
The p value for advertising comes out to be 0.970 which is higher than the level of significance
and therefore, null hypothesis would not be rejected. The conclusion can be made that
advertising is statistically insignificant to sales (Fehr and Grossman, 2013).
(d) As per above discussion, the insignificant variable is advertising and hence, would be
eliminated for the new model.
Regression model
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(e) Slope coefficient comes out to be 41.60. It indicates that if the price is increased by $ 1,
then the corresponding increase in sales would be 41.60 units (Eriksson and Kovalainen,
2015).
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Reference
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research. 3rd ed.
London: Sage Publications.
Fehr, F. H. and Grossman, G. (2013) An introduction to sets, probability and hypothesis testing.
3rd ed. Ohio: Heath.
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of
business research methods. 2nd ed. New York: Routledge.
Harmon, M. (2016) Hypothesis Testing in Excel - The Excel Statistical Master. 7th ed. Florida:
Mark Harmon.
Hillier, F. (2016) Introduction to Operations Research. 6th ed. New York: McGraw Hill
Publications.
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