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HI6007 Statistics For Shape Being Asymmetric And Values

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HI6007 Statistics For Shape Being Asymmetric And Values

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Course Code: HI6007
University: Holmes Institute

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Country: Australia

Questions:
 

a. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.
 
b. Construct a histogram showing the percent frequency distribution of the furnitureorder values in the sample. Comment on the shape of the distribution. 
 
c. Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?

Answer:

For the given data set the frequency distribution is represented in the table given below 

For the percentage frequency of the data, the histogram is represented below: 

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)

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 central tendency would be median which does not get impacted by outlier data (Hillier, 2016).

Question 2
ANOVA 

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). 

Coefficient of determination for the given case  

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). 
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). 
ANOVA 
The regression equation based on the above shown output.  

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). 

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  .
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). 

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). 

From the above, the regression line equation can be written as shown below: 

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. 
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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