Nature of Data

Statistical analysis is an important component for business intelligence. Statistical analysis assists in scrutinizing every data sample in data sets from which samples are drawn (Chen et al., 2012, p.16). The process of statistical analysis entail description of the nature of data that is chosen for analysis, investigating the relationships of data in the primary population, creation of models to assist in summarizing the comprehension of how data relates to the primary population, proving the data validity and employing analytics that is predictive to run the different states which will assist in upcoming events.

A data set is a collection of discrete items that contain related data which can be accessed exclusively or in combination or managed as a complete unit (Johnson &Wichen, 2014, p.5). Datasets are organized into some type of data structure such as a collection of business data.

On the other hand, a variable is a number, quantity or a characteristic which either increase or decreases over time (Johnson & Wichen, 2014, p.5). Moreover, it takes different values in different situations.

How to summarize a variable and the relationship between

Based on its nature, a variable can be summarized in various ways. A variable can either be discrete or continuous. Discrete variables can be summarized using frequency distribution tables and graphical summaries such as bar charts, histograms. On the other hand, continuous variables can be summarized using descriptive statistics which entail the means, standard deviations, variances, standard errors, range, mode, and median among others.

Consideration of two variables entails the nature of the variable. That is, whether the variable is categorical or quantitative. When comparing the relationship between two variables, which are categorical in nature, the analysis is made on the relationship during an assessment of conditional probabilities. Furthermore a graphical representation is made of the data using contingency tables. Such categorical variables can include class standings and gender.  When both variables are quantitative, the analysis is made on how one of the variables, the response variable, changes with respect to the changes of the other variable, the explanatory variable. To show the relationship graphically, scatter plots are used. The last scenario is when one of the variables is categorical while the other is quantitative. A good example is between gender and height. In this scenario, the comparison is best made using side-by-side box plots which show whichever similarities or differences in the center and the changeability of the variable which is quantitative across the categories.

Variables and their Summarization

why is important to be able to find patterns in a dataset using a computer

Finding patterns in a dataset is very vital in numerous ways. For starters, the pattern can be used to find inherent regularities in a data set. On the other hand, the pattern can be used as a foundation for various essential tasks. Such tasks include correlation, association, causality analysis, mining sequential, pattern analysis in stream and time series data, structural patterns, for categorization through discriminative analysis that is based on patterns, and cluster analysis through subspace clustering that is based on patterns. As a result, pattern finding in a dataset using computers has a broad application in cross-marketing, catalog design, market basket analysis, web log analysis, sale campaign analysis, and biological sequence analysis.

From the figure 1 above, it can be seen that the base selling price of size 10 cars is $19,253.For every increase in distance traveled, the selling price of the size 10 cars decreased with 0.158 units all other factors held constant. Thus, there is a negative relationship between the selling price and the distance traveled.

1. The predicted selling price when the distance travelled is 30,000km from the linear regression in part (a) is;

Predicted selling price = -0.1585*30,000+19,253 = $14,498

Thus, when a car travels 30,000 km, the selling price of the car will be $14,498.

1. Z-score of estimate:

The average of all the 10,000 estimates is 14000 with standard deviation 392.

So the z-score for sample 1 estimate is   (14,498-14000)/392= 1.265

1. P (z-score);

Using wolframalpha.com P(Z<1.265)=0.8972

1. Rank;

So if you compare sample 107 to the 10,000 samples then
Predicted rank = P(Z<z-score)*10000=0.8972*10,000=8,972

Thus, the estimate would rank at 8,972 out of 10,000.

Which sample?	107
Count of Do they like it? (y=yes, n=no)	Column Labels
Row Labels	N	y	Grand Total
A	11	67	78
B	24	90	114
Grand Total	35	157	192
Which sample?	107
Count of Do they like it? (y=yes, n=no)	Column Labels
Row Labels	N	y	Grand Total
A	14.10%	85.90%	100.00%
B	30.77%	78.95%	100.00%
Grand Total	18.23%	81.77%	100.00%

1. From the figure 2 above, it can be seen that most people in the sample prefer version A compared to B.
3. Using the sample 107 the estimated difference in proportions for p1 – p2 is 8590 – 0.7895 = 0.0695
4. The average of the 1000 sample estimates is 1 with standard deviation 0.0505.

So the z-score for that estimate in sample 107 is (0.0695 – 0.1) / 0.0505 = – 0.60

• Using wolframlapha.com

P (Z < z-score) = P( Z < – 0.60) = 0.274

1. So when you compare sample 107 to the 1000 other samples you predict the rank to be
   274 * 1000 = 274
2. e) To test the claim that there is a difference in proportions, the following hypothesis was formulated:
3. Hypothesis;

H0: There is no difference between the proportions, p1 = p2

H1: There is a difference between the proportions, p1 ≠p2

1. The resultant p-value from www.epitools.com is 0.2205.

• Since the p-value is greater than 0.05, we do not reject the H0.

1. Thus, there is strong evidence which shows that there is no difference between the sample proportions.

1. Table 2: Sample 107 summary statistics

Which sample?	107
	Values
Row Labels	Count of which machine?  (A or B)	Average of $ Casino profit from bet	StdDev of $ Casino profit from bet
A	105	0.142857143	4.539206495
B	95	-0.010526316	1.425413242
Grand Total	200	0.07	3.425458925

From the table 2 above, it can be seen that machine A had an average profit of 0.14 while machine B made a loss averaging 0.01. On the other hand, the profits from machine A had a large spread of 4.54 while machine B had a lower spread of 1.42 compared to machine A.

So for sample 107 the estimate of the difference in the population means is the difference in the sample means;= 0.143 – – 0.011 = 0.154

1. The average of the 2000  sample estimates is 4 with standard deviation 0.46 so the z-score of the sample 100 estimate is  = (0.154 – 0.4) /0.46 = – 0.535

• Using wolframalpha.com P (Z < z-score) = P (Z < – 0.535) = 0.296

1. So if you compare the sample estimate 700 to the 2000 other sample estimates  you expect it to have rank 1000 * 0.295 = 296
2. To test the claim that there is a difference in means, the following hypothesis was formulated:
3. H0: There is no difference in the sample proportions p1 = p2

H1: There is a difference in the sample proportions p1 ≠p2

1. The resultant p-value from www.epitools.com is 0.5035.

• Since the p-value is greater than 0.05, we do not reject the H0.

1. Thus, there is strong evidence which shows that there is no difference between proportions.

Description of each variable

The figure above is a back to back histogram showing the frequency of terms used by students and the administration. The x-axis is a dummy variable that shows whether the variable is a student or n administrator. The x-axis answers the question, “is the participant a student or in administration?” Thus, it is categorical n nature.

Relationship between the variables

The y-axis is the frequency of the terms that are used by either the administration or the students. It answers the question, “How often do you use the following term?” Thus, it is quantitative in nature.

Based on the bars on the right side of the back to back histogram, one can see a curved pattern. On the left side, a jagged pattern is observed. Thus, it is evident that the terms used by the students and the administration staff do not quite match in frequency. However, long bars are at the bottom while the short bars are t the top thereby implying that the discrepancies are not very big.

Would a business be able to use back to back histogram?

No. A business would not use a back to back histogram. Though back to back histograms are visually strong and can compare to normal curves, they cannot read exact values of variables since the data is grouped into categories. As a result, it will be difficult to compare two data sets.

Section 6

1. Sample 107

Sample	107
Row Labels	Count of do you support proposed change?
No	80
Yes	112
Grand Total	192

1. Sample size n is 192, Sample  proportion of people that say yes is = 112 / 192 = 0.5833
3. The average of the 1000 estimates is 6 with standard deviation 0.0357

So the z-score of the sample 700 estimate is = (0.5833 – 0.6) / 0.0357 = – 0.468

1. Using wolframalpha.com P (Z < z-score) = P (Z < – 0.468 ) = 0.320

• So if we compare sample 700 to the 1000 other estimates then we expect the rank to be
  320 * 1000 = 320

1. Find 95% confidence interval for proportion
   using wolframalpha.com, the 95% confidence interval for the proportion is 0.5136 to 0.653.

Reference:

Chen, H., Chiang, R.H. and Storey, V.C., 2012. Business intelligence and analytics: From big data to big impact. MIS quarterly, 36(4).

Johnson, R.A. and Wichern, D.W., 2014. Applied multivariate statistical analysis (Vol. 4). New Jersey: Prentice-Hall.