Table 1: A table of Frequency distribution, relative frequency distribution and percent frequency distribution
|
Width |
Frequency |
Relative Frequency |
Cumulative Relative Frequency |
Percent |
Cumulative percent |
|
150 |
3 |
0.06 |
0.06 |
6.00% |
6.00% |
|
200 |
15 |
0.3 |
0.36 |
30.00% |
36.00% |
|
250 |
14 |
0.28 |
0.64 |
28.00% |
64.00% |
|
300 |
6 |
0.12 |
0.76 |
12.00% |
76.00% |
|
350 |
4 |
0.08 |
0.84 |
8.00% |
84.00% |
|
400 |
3 |
0.06 |
0.9 |
6.00% |
90.00% |
|
450 |
3 |
0.06 |
0.96 |
6.00% |
96.00% |
|
500 |
2 |
0.04 |
1 |
4.00% |
100.00% |
|
More |
0 |
0 |
1 |
0.00% |
100.00% |
According to the frequency table above, most of the shipping charges are below 250 dollars per furniture order. Based on the cumulative percentage column, more than 50% of the shipping charges selected are below that threshold. Prices between 150 and 200 have the highest frequency of 30% followed by prices between 200 and 250 with 28% then prices between 250 and 300 which takes 12%. Cumulatively, 70% of the furniture shipping charges selected at random are between 150 and 300. The width between 450 and 500 has the least frequency of 2 price values which accounts for 4%(Siegel, 2012).
Figure 1: A Histogram plot of shipping charges for percent frequencies
The histogram plot above shows the distribution of furniture shipping charges based on mail-order business owned by Missy Walters which are presented in percentages. Generally, the data is highly skewed to the right with most of the furniture shipping prices ranging between 150 and 300 – although the prices vary from 123 to 490. Therefore, we can conclude that furniture shipping prices is not normally distributed. Close to 30% of the customers will pay approximate shipping prices of more than 350 dollars while approximately 70% would pay below 350 dollars for every shipment.
In such as sscenario where the data is not approximately normal, mean is not the best measure of central tendency. Median and mode can be used to explain the best central measure, with mode being used in discrete data where one value has a very high frequency. Median will be the best measure of central location and quartiles to evaluate the dispersion of the values. The median statistic is $228.5, first quartile is $182.75 and third quartile is $295.25.
Figure 2: Computer output for regression analysis between Demand and unit price
Demand is the response variable and unit price is the predictor
The Beta coefficient associated with the unit price in the regression output is -2.137 and a standard error of 0.248. The beta coefficient of the unit price is negative showing that increasing the price of the commodity leads to reduced demand and vice versa. To test its significance, we calculate its Z statistic and check the p-value to make the decision. Small p-values which are less the significance level shows that the variables is a significant predictor in the model(Aiken, West, & Pitts, 2003).
Since the p-value is very small, the unit price is a significant predictor of demand. Therefore, we conclude that demand and unit price are significantly related and the unit price can be used to predict the level of demand.
Coefficient of determination is a statistic which is used to evaluate the significance of a model in terms of the level of variation which can be explained by the set of predictors. It ranges between 0 and 1 and higher values symbolize a better model. This statistic is calculated using the formula below. It mostly referred to as the R-squared statistic(Devore, 2006).
According to this model, approximately 62% of the variation in demand of a product can be explained by unit price. Therefore, unit price is a very significant predictor of demand and can be solely used to explain demand to a significant percentage(Aczel & Sounderpandian, 2008).
The coeffient is correlation is calculated by taking the square root of the R-squared statistic as shown below.
There is a strong negative relationship between unit price and demand. We conclude that the relationship is negative because the model coefficient associated with unit price is negative. Therefore, as the price increases, the demand of the product reduces. This is because most people will be willing to buy products with low prices compared with pricy products(Siegel, 2012).
Figure 3: One way ANOVA model computer output for three treatments
There are three treatments and The formula of degrees of freedom is total degrees freedom is the total to obtain the error degree of freedom is
3-1+2
The total degrees freedom is 23, so we subtract the degrees of freedom due tom treatment from the total to obtain the error degree of freedom
The treatments are significantly different at 95% confidence level because the calculated F statistic is greater that the F critical value with 2 and 21 degrees of freedom. Therefore, the effect of each of the three treatments is different, hence the significantly different means for the three populations(Aiken et al., 2003).
Figure 4: Multiple linear regression computer output
Which is the number of predictors on the model
The degrees of freedom for the numerators in the calculation above for the f value are 2 and the denominator are 4(Seltman;Howard, 2017).
The calculated F value is greater than the F critical value at 2 and 4 degrees of freedom. Therefore, we conclude that the multiple regression models for predicting phones sold per day using price and number of advertising spots.
Z value for price coefficient
P-Value=0.1401
Price Coefficient in the model is not statistically different from zero at 95% confidence level, because the p-value is greater than the significance level of 0.05.
The p-value is very small, hence the conclusion that number of advertising spots coefficient is statistically difference from zero(Huberty, 2003).
Increasing the number of advertising spots by one, the number of mobile phones sold in a day will increase by 0.4733.
10 advertisement spots and $20,000 per phone
Around 16 phones shall be sold for $20,000 per phone and using10 advertising spots.
References
Aczel, A. D., & Sounderpandian, J. (2008). Complete: Business Statistics. ASSOCIATION OF BUSINESS INFORMATION …. Retrieved from https://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:McGraw-Hill/Irwin+=%3E?#1
Aiken, L. S., West, S. G., & Pitts, S. C. (2003). Multiple Linear Regression. Handbook of Psychology, 481–507. https://doi.org/10.1051/eas/1466005
Devore, J. (2006). Statistics for Business and Economics. The American Statistician, 60(4), 342–343. https://doi.org/10.1198/tas.2006.s59
Huberty, C. J. (2003). Multiple correlation versus multiple regression. Educational and Psychological Measurement, 63(2), 271–278. https://doi.org/10.1177/0013164402250990
Seltman;Howard. (2017). One-Way ANOVA. Experimental Design and Analysis, 171–190. Retrieved from https://www.jmp.com/content/dam/jmp/documents/en/academic/learning-library/04-one-way-anova.pdf
Siegel, A. F. (2012). Practical Business Statistics. Practical Business Statistics. https://doi.org/10.1016/B978-0-12-385208-3.00014-6
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