Statistics Assignment Solution: Frequency, Regression, ANOVA

This document presents a complete solution to a statistics assignment, addressing key statistical concepts and methods. The solution begins with an analysis of frequency tables and histograms, including interpretations of skewness and the selection of appropriate central tendency measures. It then delves into regression models, covering hypothesis testing for slope coefficients, the calculation and interpretation of the coefficient of determination and correlation, and the significance of the linear relationship between variables. The assignment also explores ANOVA (Analysis of Variance) tables, providing test statistics, p-values, and conclusions regarding the equality of means across different populations. Finally, the solution encompasses multiple regression models, including the derivation of regression equations, hypothesis testing for multiple regression models, and interpretations of slope coefficients for various predictor variables, such as advertising spots, and mobile price. The assignment is supported by relevant references.

STATISTICS
H16007 STATISTICS
ASSIGNMENT
Student Name
[Pick the date]
Question 1

(a) Frequency table
Normal view of frequency table
Formula view of frequency table
(b) Histogram
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The asymmetric shape of the histogram indicated above is established from the length of the
right tail exceeding that of the left tail. This corresponds to presence of positive skew and
potential presence of positive side outliers (Taylor and Cihon, 2014).
(c) The suitable central tendency measure needs to be outlined. The choice is between mean and
median. Here, median would be the appropriate choice considering that the underlying data is
skewed and hence the mean would be vulnerable to extremely high values which is not an
issue with median (Lehman and Romano, 2016).
Question 2
Regression Model
Normal view of regression model
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Formula view of regression model
(a) The relevant hypotheses for performing hypothesis test are listed below.
The slope coefficient corresponding to unit price has a test statistics value of -8.617 which yields
the p value as 0.000. Thus, the evidence indicates rejection of H0 thus paving way for acceptance
of H1 (Koch, 2013).
Conclusion: The linear relationship between the two variables is significant in statistical terms
owing to slope being non-zero.
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(b) For the regression model, the coefficient of determination is determined as highlighted
below:
The given regression model has the capability to account to explain 61.7% changes in the unit
demand using price as the suitable predictor variable (Harmon, 2011).
(c) For the regression model, the coefficient of correlation is determined as highlighted below:
Considering the above computations, the appropriate value of correlation coefficient is -0.786
and this value has been selected considering that regression line is downward sloping as evident
from the slope (Lind, Marchal and Wathen, 2012).
Question 3
Normal view of ANOVA table
Formula view of ANOVA table
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Test statistics (For ANOVA based on the above output) = 25.89
Corresponding p value (For ANOVA based on the above output) = 0.00
Conclusion: It would not be appropriate that the means across the different populations is same
as the statistical evidence suggests that one least one population mean shows a significant
deviation (Koch, 2013).
Question 4
Normal view of Regression model
Formula view of Regression model
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(a) Regression equation based on intercept and slope coefficients is given below:
(b) Total data has taken for one week i.e. for n = 7 days and hence,
The degree of freedom (Regression) = k = 2
The degree of freedom (Residual) = 7-2-1 =4
The relevant hypotheses for performing hypothesis test are listed below.
Test statistics (For ANOVA based on the above output) = 80.118
Corresponding p value (For ANOVA based on the above output) = 0.00
Conclusion: The multiple regression model highlighted above is significant owing to existence of
atleast one non-zero slope coefficient.
(c)
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For mobile price:
The slope coefficient corresponding to unit price has a test statistics value of 1.078 which yields
the p value as 0.206. Thus, the evidence indicates non-rejection of H0.
Conclusion: The linear relationship between the two variables is insignificant in statistical terms
owing to slope being assumed as zero.
The slope coefficient corresponding to unit price has a test statistics value of 12.23 which yields
the p value as 0.000. Thus, the evidence indicates rejection of H0 thus paving way for acceptance
of H1.
Conclusion: The linear relationship between the two variables is significant in statistical terms
owing to slope being non-zero.
(d) Slope coefficient for advertising spots : = 0.4733
Interpretation: The above coefficient highlights that daily sales of mobile can witness an
increase/decrease of 0.4733 units provided the advertising spots undergo an increase/decrease of
1 unit (Harmon, 2011).
(e) Regression equation
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Inputs:
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References
Harmon, M. (2011) Hypothesis Testing in Excel - The Excel Statistical Master 7th ed. Florida:
Mark Harmon.
Koch, K.R. (2013) Parameter Estimation and Hypothesis Testing in Linear Models 2nd ed.
London: Springer Science & Business Media.
Lehman, L. E. and Romano, P. J. (2016) Testing Statistical Hypotheses 3rd ed. Berlin : Springer
Science & Business Media.
Lind, A.D., Marchal, G.W. and Wathen, A.S. (2012) Statistical Techniques in Business and
Economics 15th ed. New York: McGraw-Hill/Irwin.
Taylor, K. J. and Cihon, C. (2014) Statistical Techniques for Data Analysis 2nd ed. Melbourne:
CRC Press.
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