Statistics Assignment: Data Analysis, ANOVA, Regression Analysis

This statistics assignment solution covers various aspects of statistical analysis. The solution begins with frequency distribution and histogram analysis, including identification of outliers based on skewness. It then proceeds to ANOVA, testing the relationship between variables like demand and unit price, and determining the coefficient of determination and correlation. Further, the solution involves ANOVA to compare population means and multiple linear regression analysis, including the regression equation, significance tests for variables (mobile phone price and advertising spots), and interpretation of slope coefficients. Finally, the solution provides a regression line equation and predicts daily sales based on price and advertising spots. References from academic sources are included to support the analysis.

STATISTICS
ASSIGNMENT
Student Name
[Pick the date]
Question 1

(a) For the given data set the frequency distribution is represented in the table given below:
(b) For the percentage frequency of the data, the histogram is represented below:
(c) The graph has an asymmetric shape viewing the unequal length of the tail on either sides. For
a symmetric graph these have to be equal. Owing to the shape being asymmetric, the values
on the right end such as in excess of $ 450 can be outliers or abnormal values (Hillier, 2016)
(d) The mean is considered to be the default measure of central tendency but this assumption
holds true only when the data is not skewed. In the presence of skew, the mean can be
potentially leading due to the effect of the extreme values. Hence, a better choice to represent
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central tendency would be median which does not get impacted by outlier data (Hillier,
2016).
Question 2
ANOVA
(a) Test to find the presence of relation between variable 1 (Demand) and variable 2 (unit price)
Assuming alpha = 0.05 or 5%
The p value with respect to the t value comes out to be 0.000.
Here, and this lead rejection of and acceptance of
Since, slope cannot be taken as zero, hence it implies the linear relationship between the
variables is significant and cannot be ignored (Koch, 2013).
(b) Coefficient of determination for the given case
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The above value symbolises the ability of the independent variable i.e. unit price to be able to
account for 61.7% of the variation highlighted in the dependent variable i.e. demand. The
remaining variation remains unexplained for which an additional independent variable might
need to be inserted (Harmon, 2015).
(c) Coefficient of correlation for the given case
The appropriate correlation coefficient can be chosen considering whether the relationship
between the given variables is directly proportional or inversely proportion. The slope of
regression line is negative thus confirming that the relationship is indeed inversely proportional
and hence the coefficient of correlation would be -0.786 (Hillier, 2016).
Question 3
ANOVA
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Assuming alpha = 0.05 or 5%
The p value with respect to the F value comes out to be 0.000.
Here, and this lead rejection of and acceptance of
Clearly, all the population means are not the same and there is significant deviation in atleast one
population mean from the remaining means (Koch, 2013).
Question 4
ANOVA
(a)
The regression equation based on the above shown output.
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(b) The day is gathered for seven days (n =7). Degree of freedom in case of regression would be
(k=2) 2 and in case of residual would be (n-k-1) =4.
Assuming alpha = 0.05 or 5%
The p value with respect to the F value comes out to be 0.000.
Here, and this lead rejection of and acceptance of
The null hypothesis rejection highlights the statistical significance of the multiple liner
regression model since both the slopes are not insignificant (Harmon, 2015).
(c) Significance test for variable 1 (Mobile phone price)
Assuming alpha = 0.05 or 5%
The p value with respect to the t value does not come out to be zero and has a significant value of
0.2060.
Here, and this does not result in rejection of .
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Non-rejection of null hypothesis leads to conclusion that the value of slope can be taken as zero
implying relationship not being significant between price and sales (Koch, 2013).
Similarly,
Significance test for variable 2 (Mobile phone advertising spots)
Assuming alpha = 0.05 or 5%
The p value with respect to the t value comes out to be zero.
Here, and this leads rejection of and acceptance of
Rejection of null hypothesis leads to conclusion that the value of slope cannot be taken as zero
implying relationship being significant between advertisement spots and sales (Hillier, 2016).
(d) The slope coefficient for variable 2 (advertising spots ) is shown below:
Β advertising spots = 0.4733
Interpretation: The positive sign associated with the slope highlights that a proportional
relationship exists between the given variables. Further, the magnitude highlights that if the
advertising spots are increased or decreased by 1 unit, then the daily sales of mobile would also
be expected to increase or decrease by 0.4733 units (Koch, 2013).
(e) From the above, the regression line equation can be written as shown below:
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Variable 1
Variable 2
Therefore,
Company would be able to clock a daily sales of 9,960 mobiles phone for a price of $20,000 and
after doing 10 advertising spots.
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References
Harmon, M. (2015). 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.
Koch, K.R. (2013). Parameter Estimation and Hypothesis Testing in Linear Models (2nd ed.).
London: Springer Science & Business Media.
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