# Statistics: Confidence Intervals and Regression Essay

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Updated: Apr 12th, 2021

## Confidence Intervals

There are many concepts in statistics that are used in order to increase the chance to find the right result. The use of confidence intervals can be listed among important estimates helping to solve problems in statistics. In reference to the meaning of a confidence interval in the context of problems in statistics, it needs to be said that this tool is often referred to as the value that can help to indicate the degree to which measurements and data that has been collected are accurate. In real life, confidence intervals for proportions can be used by companies that produce and sell clothes to make more accurate guesses concerning the sizes needed.

In reference to the significance of the tool under analysis and the degree to which it helps to solve problems, a confidence interval can also act as a tool that indicates the extent to which the calculated values are stable. Thus, indicating the degree of stability of some value, a confidence interval can be used to make assumptions concerning the results of further identical experiments that can be conducted.

In this case, a confidence interval is used to predict the difference between results retrieved with the help of two experiments that are performed with the use of the same materials and experimental conditions. A confidence interval belongs to the number of interval estimates that are widely used in statistics, and, due to the relative complexity of the tool under consideration, there is a limited opportunity to use this tool in real life in order to solve everyday tasks.

As is clear from the example proposed in the eighth chapter, a confidence interval for a population mean can be used in statistics to define the degree to which products, people, or organizations comply with accepted rules and adhere to specific standards (Bowerman et al. 294). Even though a confidence interval is ranked among the tools that are primarily used to solve the specific statistical problem, it can also be possible to use it in real life to be more effective at performing everyday tasks. Among the examples of how confidence intervals for proportions can be used in the real world is the working process in companies related to the clothing industry.

Clothing manufacturers and family clothing stores that appeal to a broader market never know the clothing size of people who are going to buy their apparel products. Due to that, any company that manufactures apparel or sells it, collaborating with suppliers, should know how many pieces of clothing should be manufactured or purchased to sell the largest possible number of goods. Using the data on the sizes of clothes from the previous collections that have been sold in a certain country or city, companies in the clothing industry can find the mean values and consider the sizes that are the least popular among customers.

Having defined the most popular sizes based on this data, it is possible to calculate a confidence interval indicating the accuracy of assumptions. Therefore, companies will study the population and the degree to which different sizes are popular, and it will allow increasing profits.

Using confidence intervals in real life has certain advantages, and this tool helps manufacturers to define whether they have accurate data on the needs of the target audience and, therefore, decrease the number of unsold clothes whose price will need to be reduced. At the same time, there are some cons associated with the use of confidence intervals in real life. For instance, the tool does not produce credible results if it is used with a small sample, and this is why the number of situations when it can be successfully applied is limited. Personally, I believe that the use of this tool in real life requires in-depth knowledge concerning proper sampling techniques as well.

## Regression

Regression is ranked among popular statistical techniques that can be used to solve important theoretical problems. Apart from that, the use of regression that indicates the relationship between certain variables can find use in real life. For instance, the statistical technique under consideration allows people in different professional fields to define actions and innovations that have a significant impact on sales, the purchase decisions of clients, consumer preferences, the productivity of working processes, or the quality of goods.

Speaking about the ways to use simple or linear regression in the real world, this technique can be used in agricultural experiments by both manufacturers of agricultural chemicals and common allotment gardeners who would like to define the measures helping them to grow more fruits and vegetables with better physical properties.

Linear regression or simple regression presents an approach to studying the relationship between a few variables, and this tool is among the most commonly used techniques that help entrepreneurs all over the world to make decisions that increase profits and improve the quality of services and products that are offered to target customers. The use of linear regression presents a good method to indicate the relationships between dependent and independent variables because it helps to define the key tendencies and factors that impact final results and products. As it has been stated, there is plenty of everyday situations (primarily related to business) in which linear regression and its results can be used for decision-making purposes.

Linear regression can be extremely helpful in business. The example provided in the case study presented in the book indicates that linear regression is a tool that helps to define and study the factors that impact the yearly revenues of restaurants. The company from the case can use this information for many purposes, including making the decision concerning the preferred location of new restaurants (Bowerman et al. 468). Apart from that, the tool can be used in agriculture in order to assess the effectiveness of various fertilizing agents. Due to the key reason to use fertilizers, their effectiveness can be measured due to the impact that they have on the yielding capacity of horticultural crops.

To define the effectiveness of certain fertilizers (for instance, two) on their own, allotment gardeners can make three rows of tomato plants in different parts of their gardens and use two different fertilizers for the first two rows on a regular basis. Apart from that, for the sake of accuracy, no fertilizers should be used to grow the third row of tomato plants. Also, to retrieve more credible results, one needs to ensure that the use of fertilizers is the only difference in environmental conditions that can impact the growth of plants.

Collecting the data on the fertilizer used (dependent variable) and the average number of tomatoes picked from each vine (explanatory variable), it is possible to present this data with the help of a graph, indicating the changing size of the harvest and the impact of fertilizer used (Darlington and Hayes 23). Also, the approach can be applied to find out whether the frequency of fertilization has a positive impact on the yielding capacity of various orchard crops. Thus, the results of linear regression can be used for decision-making purposes in many fields of activity.

## Works Cited

Bowerman, Bruce, et al. Essentials of Business Statistics (5th ed.). McGraw-Hill Education, 2015.

Darlington, Richard B., and Andrew F. Hayes. Regression Analysis and Linear Models: Concepts, Applications, and Implementation. Guilford Publications, 2017.

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