- Frequency distribution
Table 1: Frequency distribution
|
bin
|
Frequency
|
Relative Frequency
|
Percentage
|
Cumulative Frequency
|
|
170
|
8
|
0.16
|
16%
|
16%
|
|
220
|
15
|
0.3
|
30%
|
46%
|
|
270
|
12
|
0.24
|
24%
|
70%
|
|
320
|
4
|
0.08
|
8%
|
78%
|
|
370
|
5
|
0.1
|
10%
|
88%
|
|
420
|
2
|
0.04
|
4%
|
92%
|
|
470
|
2
|
0.04
|
4%
|
96%
|
|
520
|
2
|
0.04
|
4%
|
100%
|
- Histogram of Shipping Charges showing percentages
Shipping charges are highly skewed to the right, showing that there is the extreme value of the charges. 30% of the values selected are between 170 and 220, 24% between 220 and 270 and 16% between 120 and 170. More than 50% of the values are between 120 and 270 and the maximum value is 490. Therefore, data on shipping charges are not approximately normal.
- The most appropriate measure of central tendency
The median statistic will be the best measure of central tendency because it is not much affected by extreme values.
Demand and Unit price
- Is demand and Unit Price related?
Demand is the response variable and unit price is the predictor
Since the p-value is very small, the unit price is a significant predictor of demand. Therefore, demand and unit price are significantly related.
- Coefficient of determination
61.71% of the variation experienced on the demand is explained by unit price.
- Coefficient of correlation
The coefficient of correlation is the square root of coefficient of determination
There is a strong relationship between unit price and demand with a Pearson’s correlation of 0.786.
Because the F-value is greater than the F critical value, we conclude that there is significant difference between the three treatments at 0.05 significance level.
- Regression equation
- Significance of the model
The Calculated F value is greater than the F critical value (2, 4). Therefore, we conclude that there is a statistically significant relationship between the set of independent variables and the dependent variablemultiple.
- The significance of the coefficients
- is not statistically different from zero at 0.05 significance level, because the p-value is greater.
The p-value is very small, hence the conclusion that is statistically difference from zero.
- Slope coefficient for X2
Increasing the number of advertising spots by one, the number of mobile phones sold in a day will increase by 0.4733.
- Prediction
Number of mobile phones to be sold for 10 advertisement spots and $20,000 per phone
Approximately 16 mobile phones will be sold for $20,000 per phone and 10 advertising spots.
References
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Aiken, L. S., S. G. West, and S. C. Pitts. “Multiple Linear Regression.” Handbook of Psychology, 2003, 481–507. https://doi.org/10.1051/eas/1466005.
Crawley, Michael J. “Regression.” In The R Book, 449–97, 2012. https://doi.org/10.1002/9781118448908.ch10.
Roberts, Donna. “Statistics 2 - Correlation Coefficient and Coefficient of Determination.” MathBits.com, 2013. https://mathbits.com/MathBits/TISection/Statistics2/correlation.htm.
Seltman, Howard. “One-Way ANOVA.” Experimental Design and Analysis, 2017, 171–90. https://www.jmp.com/content/dam/jmp/documents/en/academic/learning-library/04-one-way-anova.pdf.
Su, Xiaogang, Xin Yan, and Chih-Ling Tsai. “Linear Regression.” Wiley Interdisciplinary Reviews: Computational Statistics 4, no. 3 (2012): 275–94. https://doi.org/10.1002/wics.1198.
