Statistics Assignment: Regression Analysis and ANOVA Testing

This statistics assignment solution addresses key concepts in data analysis and statistical inference. The first question analyzes examination scores, assessing the distribution's normality using a histogram and identifying negative skewness. Question 2 explores regression analysis, examining the relationship between unit price and supply, calculating R-squared, and determining correlation strength. Hypothesis testing is performed, and the null hypothesis is not rejected. The assignment then delves into ANOVA tests, regression equation derivation, and hypothesis testing for regression models. It analyzes the significance of price and advertising expenditure, interpreting slope coefficients and constructing a regression model with statistically significant variables. References include Flick (2015), Hair et al. (2016), and Harmon (2016), providing a robust foundation for the statistical analyses performed.

STATISTICS
Student Name
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Question 1
(a) The frequency distribution of the examination scores
(b) Histogram for representing the examination scores percentage
The relevant observations can be extracted from the above highlighted histogram that the shape
of histogram is not bell-curve which is indicative of non-normal distribution of examination
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score. Further, high deviation has also been observed in data which is evident negative skew.
Therefore, the distribution of examination score would not be assumed to be normal distributed
(Flick, 2015).
Question 2
(a) Unit price is represented as x and supply is represented as y.
ANOVA table Normal and formula view
(a) The sample size = 1 + (Degree of freedom) = 1 + (36+1) = 41
(b) Null and alternative hypothesis
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Slope coefficient =0.029
The p value = 0.175
Significance level = 5% or 0.05
Visibly, the p value is more than significance level and hence, null hypothesis will not be
rejected. Therefore, the variables supply and unit prices are not correlated (Flick, 2015).
(c) R square
Sum of squares regression= 354.689
Sum of squares of error = 7035.262
Total sum of squares = (354.689)+(7035.262) = 7389.95
Now,
R square (Coefficient of determination) = Sum of squares regression/ Total sum of squares =
0.048 or 4.8%
R square is indicates that that 4.8% deviation in supply will be described by deviation in unit
price. This percentage is quite insignificant (low) and hence, the regression model does not
constitute as good fit model (Harmon, 2016).
(d) R
The square root of coefficient of determination is termed as correlation coefficient. The sign of
the correlation coefficient is decided based on the sign of slope coefficient. It is apparent that
slope is position and therefore, the coefficient of correlation would also be positive (Hair, et.al.,
2016).
R = 0.219
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The value of R is inferior than 0.5 and therefore, the correlation strength between supply and unit
price is not strong and would be assumed to be weak only (Harmon, 2016).
(e) The regression line equation can be written as highlighted below.
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Question 3
ANOVA single factor test output
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Question 4
(a) The description of variables and regression output
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Regression equation
Y =3.598+ ( 41.320 X 1 ) +(0.013 X 2)
(b) Hypothesis testing for regression model
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(c) Hypothesis testing for slopes
Relevant part of regression
Significance level (Alpha) = 0.10
Slope coefficient: Price (X1)
Observation: The p value < level of significance (0.036 <0.1)
Result: “Reject the null hypothesis and accept alternative hypothesis (Flick, 2015).”
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Summary: “Price is significant for the regression model. It means that statistically sale is
correlated with the price.”
Slope coefficient: Advertising Expenditure (X2)
Observation: The p value > level of significance (0.97 >0.1)
Result: “Fails to reject the null hypothesis and hence, cannot accept alternative hypothesis
(Harmon, 2016).”
Summary: “Advertising expenditure is insignificant for the regression model.”
(d) Insignificance variable =Advertising expenditure
Regression model only with statistically significant variable
Regression equation
Y =3.582+ ( 41.603 X 1 )
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(e) Interpretation of slope:
The slope coefficient implies that change in sales to the tune of 41.60 units can be produced by a
unit change in price. Further, the direction of change for both variables would be same as slope is
positive.
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Reference
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. (2016) 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.
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