Simple Linear Regression Model

This article considers the relationship between two variables in two ways: (1) by using regression analysis and (2) by computing the correlation coefficient. By using the regression model, we can evaluate the magnitude of change in one variable due to a certain change in another variable. For example, an economist can estimate the amount of change in food expenditure due to a certain change in the income of a household by using the regression model.

A sociologist may want to estimate the increase in the crime rate due to a particular increase in the unemployment rate. Besides answering these questions, a regression model also helps predict the value of one variable for a given value of another variable. For example, by using the regression line, we can predict the (approximate) food expenditure of a household with a given income. The correlation coefficient, on the other hand, simply tells us how strongly two variables are related.

It does not provide any information about the size of the change in one variable as a result of a certain change in the other variable. Let us return to the example of an economist investigating the relationship between food expenditure and income. What factors or variables does a household consider when deciding how much money it should spend on food every week or every month? Certainly, income of the household is one factor. However, many other variables also affect food expenditure.

For instance, the assets owned by the household, the size of the household, the preferences and tastes of household members, and any special dietary needs of household members are some of the variables that influence a household’s decision about food expenditure. These variables are called independent or explanatory variables because they all vary independently, and they explain the variation in food expenditures among different households. In other words, these variables explain why different households spend different amounts of money on food.

Food expenditure is called the dependent variable because it depends on the independent variables. Studying the effect of two or more independent variables on a dependent variable using regression analysis is called multiple regressions. However, if we choose only one (usually the most important) independent variable and study the effect of that single variable on a dependent variable, it is called a simple regression. Thus, a simple regression includes only two variables: one independent and one dependent. Note that whether it is a simple or a multiple regression analysis, it always includes one and only one dependent variable.

It is the number of independent variables that changes in simple and multiple regressions. The relationship between 2 variables in a regression analysis is expressed by a mathematical equation called a regression equation or model. A regression equation, when plotted, may assume one of many possible shapes, including a straight line. A regression equation that gives a straight-line relationship between two variables is called a linear regression model; otherwise, the model is called a nonlinear regression model.

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The Poisson Probability Distribution

The Poisson probability distribution, named after the French mathematician Simeon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson probability distribution terminology.

The Poisson probability distribution is applied to experiments with random and independent occurrences. The occurrences are random in the sense that they do not follow any pattern, and, hence, they are unpredictable. Independence of occurrences means that one occurrence (or nonoccurrence) of an event does not influence the successive occurrences or nonoccurrences of that event. The occurrences are always considered with respect to an interval. In the example of the washing machine, the interval is one month. The interval may be a time interval, a space interval, or a volume interval.

The actual number of occurrences within an interval is random and independent. If the average number of occurrences for a given interval is known, then by using the Poisson probability distribution, we can compute the probability of a certain number of occurrences, x, in that interval. Note that the number of actual occurrences in an interval is denoted by x. The following three conditions must be satisfied to apply the Poisson probability distribution. 1. x is a discrete random variable. 2. The occurrences are random. 3. The occurrences are independent.

The following are three examples of discrete random variables for which the occurrences are random and independent. Hence, these are examples to which the Poisson probability distribution can be applied. 1. Consider the number of telemarketing phone calls received by a household during a given day. In this example, the receiving of a telemarketing phone call by a household is called an occurrence, the interval is one day (an interval of time), and the occurrences are random (that is, there is no specified time for such a phone call to come in) and discrete.

The total number of telemarketing phone calls received by a household during a given day may be 0, 1, 2, 3, 4, and so forth. The independence of occurrences in this example means that the telemarketing phone calls are received individually and none of two (or more) of these phone calls are related. 2. Consider the number of defective items in the next 100 items manufactured on a machine. In this case, the interval is a volume interval (100 items).

The occurrences (number of defective items) are random and discrete because there may be 0, 1, 2, 3, … , 100 defective items in 100 items. We can assume the occurrence of defective items to be independent of one another. 3. Consider the number of defects in a 5-foot-long iron rod. The interval, in this example, is a space interval (5 feet). The occurrences (defects) are random because there may be any number of defects in a 5-foot iron rod. We can assume that these defects are independent of one another.

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Expansion Devices

Page 1 of 4 Expansion Devices I. Introduction Expansion devices are basic components of a refrigeration system which carry out two major purposes: (1) the pressure reduction from the condenser to evaporator pressure and (2) the regulation of refrigerant flow into the evaporator. These expansion devices can be generally classified into two types which are namely the fixed opening type (flow area is fixed) and the variable opening type (flow area changes correspondingly with a change in mass flow rates).

There are about seven basic types of expansion devices for a refrigerant in a refrigeration system. These include capillary tubes and orifice which are under the fixed opening type and the manual expansion valves, automatic expansion valve (AEV), thermostatic expansion valve (TEV), electronic expansion valve and float type expansion valve which are all under the variable opening type. The float type expansion valve is further classified into high side float valve and low side float valve (Arora, 2006).

One of the most commonly used expansion device is the capillary tube. For the purpose of this exercise, a computation related to it will be performed. In a lesson guide on expansion devices prepared by Prof. R. C. Arora in 2006, he/she defined a capillary tube as “…a long, narrow tube of constant diameter. The word „capillary? is a misnomer since surface tension is not important in refrigeration application of capillary tubes. Typical tube diameters of refrigerant capillary tubes range from 0. 5 mm to 3 mm and the lengths range from 1. 0 m to 6 m. II. Objectives The exercise was conducted to familiarize the students with expansion devices, its functions and its importance. Specifically, the objectives were: 1. ) to examine the construction of some commonly-used expansion devices; and 2. ) to assess the performance of some commonly-used expansion devices. III. Methodology A. Lab-Scale Refrigeration System A lab-scale set-up for a refrigeration system in the refrigeration laboratory was observed for the effects of expansion devices on the pressures at various points within the system.

Three different types of expansion devices which are namely the capillary, constant-pressure and thermostatic expansion devices are activated by opening their corresponding valves. The reading at each of the five pressure reading points was recorded for every 2 to 3 minutes until they become stable. An image of the observed set- Page 2 of 4 up was taken and the locations of the pressure-reading points were labelled. See Appendix A for the image. B. Computation: Capillary Tube For the stabilized values of the condenser and evaporator pressures measured, the required theoretical length of the capillary tube was computed.

The results were then compared with the actual length of the capillary tube observed in the laboratory. See Appendix B for the value of the computed and measured length of capillary tube. IV. Answers to Questions 1. In the computation part above, is there a discrepancy between the actual and the calculated length of capillary tube? Explain. Based on Table 1, there is a discrepancy between the computed and measured value of the capillary tube. First, it must be noted that throughout the computation, assumptions were made.

Upon realizing the difficulty of obtaining a value for the mass flow rate, a reasonable value of it was assumed. This could affect the obtained theoretical length of capillary tube since some of the parameters involved in the computation require its use. Simply said, the theoretical length would either increase or decrease depending on the assumed value but never equal to the actual length, unless the same mass flow rate completely applies to the actual system (which might not really be the case).

This is the same explanation behind the other assumed parameters. Additionally, the measurement of quantities necessary for computing the length of capillary tube is also subject to many possible errors. This may include errors due to the limitation of the instruments or devices or due to some human inflicted errors. From the computed percent error, it can be inferred that the two values for capillary tube length deviate from each other at the specified percentage. V. References Arora, 2006. Expansion Devices. [pdf file] Available at . VI.

Appendix A. Figure with labels Page 3 of 4 PRESSUREREADING POINT 5 PRESSUREREADING POINT 1 PRESSUREREADING POINT 2 PRESSURE READING POINT 3 PRESSUREREADING POINT4 Fig 1. An image showing the pressure reading points in a lab-scale set-up for a refrigeration system B. Tabulated data Table 1. Measured and computed length of capillary tube Quantities Actual length (m) Theoretical length (m) Percent error (%) Values 4. 1 7. 17 42. 82 Note: Computations on how I arrived with these values are in the spreadsheet submitted with this report. Page 4 of 4

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Application of Statistical Concepts in the Determination

A skillful researcher aims to end his study with a precise and accurate result. Precision refers to the closeness of the values when some quantity is measured several times; while accuracy refers to the closeness of the values to the true value. The tool he utilizes to prevent errors in precision and accuracy is called statistics.

In order to become familiar to this tactic, the experiment aims to help the researchers become used to the concepts of statistical analysis by accurately measuring the weights of ten (10) Philippine 25-centavo coins using the analytical balance, via the “weighing by difference” method. Then, the obtained data divided into two groups and are manipulated to give statistical significance, by performing the Dixon’s Q-test, and solving for the mean, standard deviation, relative standard deviation, range, relative range, and confidence limit—all at 95% confidence level.

Finally, the results are analyzed between the two data sets in order to determine the reliability and use of each statistical function. RESULTS AND DISCUSSION This simple experiment only involved the weighing of ten 25-centavo coins that are circulating at the time of the experiment. In order to practice calculating for and validating accuracy and precision of the results, the coins were chosen randomly and without any restrictions. This would give a random set of data which would be useful, as a statistical data is best given in a case with multiple random samples.

Following the directions in the Analytical Chemistry Laboratory Manual, the coins were placed on a watch glass, using forceps to ensure stability. Each was weighed according to the “weighing by difference” method. The weighing by difference method is used when a series of samples of similar size are weighed altogether, and is recommended when the sample needed should be protected from unnecessary atmosphere exposure, such as in the case of hygroscopic materials. Also, it is used to minimize the chance of having a systematic error, which is a constant error applied to the true weight of the object by some problems with the weighing equipment.

The technique is performed with a container with the sample, in this experiment a watch glass with the coins, and a tared balance, in this case an analytical balance. The procedure is simple: place the watch glass and the coins inside the analytical balance, press ON TARE to re-zero the display, take the watch glass out, remove a coin, then put the remaining coins back in along with the watch glass. Then, the balance should give a negative reading, which is subtracted from the original 0. 0000g (TARED) to give the weight of the last coin. The procedure is repeated until the weights of all the coins are measured and recorded.

Since the number of samples is limited to 10, the Dixon’s Q-test was performed at 95% confidence level in order to look for outliers in each data set. The decision to use the Q-test despite the fact that there were only a few, limited number of samples and to use the confidence level of 95% was carried out as specified in the Laboratory Manual. Significance of Q-test The Dixon’s Q-test aims to identify and reject outliers, values that are unusually high or low and thus differ considerably from the majority and thus may be omitted from the calculations and usages in the body of data.

The Dixon’s Q-test should be performed, since a value that is extreme compared to the rest can bring inaccurate results that go against the estimated limits set by other calculations and thus affect the conclusion. This test allows us to examine if one (and only one) observation from a small set of replicate observations (typically 3 to 10) can be “legitimately” rejected or not. The outlier is classified objectively, by calculating for the suspected outlier, Qexperimental, Qexp, and comparing it with the tabulated Qtab. Qexp is determined by Qexp equation (1). Qexp=Xq-XnR (1)

Where Xq is the suspected value, Xn is the value closest to Xq, and R is the range, which is given by the highest data value subtracted by the lowest data value. R=Xhighest-Xlowest (2) If the obtained Qexp is found to be greater than Qtab, the outlier can be rejected. In the experiment, the sample calculation for Data Set 1 is given below: Qexp=Xq-XnR=3. 7549-3. 60723. 7549-3. 5574=0. 14770. 1975=0. 74785 Since Qtab for the experiment is set as 0. 625 for 6 samples at 95% confidence level, Qexp>Qtab. Thus, the suspected value 3. 7549 is rejected in the calculations for Data Set 1.

The same process was done for the lowest value of Data Set 1 and the values for Data Set 2, and the values were accepted and will be used for further calculations. This is shown in table 2. (Refer to Appendix for full calculations. ) The statistical values were then computed for the two data sets, and were compared to relate the significance of each form of statistical functions.

The values required to be calculated are the following: mean, standard deviation, relative standard deviation (in ppt), range, relative range (in ppt), and confidence limits (at 95% confidence level). Significance of the mean and standard deviation The mean is used to locate the center of distribution in a set of values [2]. By calculating for the average value of the data set, it can be determined whether the set of data obtained is close to each other or is close to the theoretical value. Thus, both accuracy and precision may be determined with the mean, coupled with other statistical references.

In the experiment, the mean was calculated using equation (3). The sample calculation used the data from Data Set 1, which had 5 samples after the outlier was rejected via the Q-test. X=i=1nXi=X1+X2+X3…+Xnn 3 =(3. 6072+3. 6002+3. 5881+3. 5944+3. 5574)5=3. 5895 Mean is represented by X, the data values by X, and the number of samples by n. It can be observed that the mean indeed shows the precision of the accumulated values, as all the values are close to each other and the mean. The standard deviation, on the other hand, is a relative measure of precision of the values.

It shows how much the values spread out from the mean. A smaller standard deviation would show that the values are relatively closer to the mean, and a bigger one would show that the values are spread out more. This does not determine the validity of the experimented values. Instead, it is used to calculate further statistical measures to validate the data. The equation (4) was used to calculate the standard deviation, where s represents standard deviation, and the rest are known from the mean. The data set used is the same as the mean. s=1n-1i=1nXi-X2 4 =15-1[3. 072-3. 58952+3. 6002-3. 58952+3. 5881-3. 58952+3. 5944-3. 58952+3. 5574-3. 58952] =0. 019262 Mean and standard deviations by themselves are relatively poor indicators of the accuracy and precision of the data. These are manipulated to give clearer views on the data. One of the measures of precision is the relative standard deviation. RSD=sX? 1000ppt (5) =0. 0192623. 5895? 1000=5. 3664 The relative standard deviation is a useful way of determining the precision of the data compared to other sets of data, as the ratio would be a good way of differentiating the two.

This will be expounded further. Range is easily found with equation (2) to give the value of 0. 0498, taking note that the highest value was rejected via the Q-test. R=3. 6072-3. 5574=0. 0498 The relative range is also a way of comparing sets of data, just like the relative standard deviation. Again, it will be discussed when comparing the values from data sets 1 and 2. RR=RX? 1000ppt (6) =0. 04983. 5895? 1000=13. 874 Significance of the confidence interval The confidence interval is used to give the range at which a given estimate may be deemed reliable.

It gives the interval in which the population mean is to be included in. The boundaries of the interval are called confidence limits, and are calculated by equation (7). Confidence limit=X±tsn 7 =3. 5895±2. 780. 0192625 =3. 5895±0. 023948 Using the confidence limit and the interval, one can easily determine the value that can be estimated if the same experiment was performed. The confidence limit shows that there is a 95% confidence that the actual mean lies between the values of 3. 5656 and 3. 6134. Difference between Data Set 1 and Data Set 2

The statistical values computed from the two data sets are arranged below in table 3. Table 3. Reported values for data sets 1 and 2| Data Set| Mean| Standard Deviation| Relative SD| Range| Relative Range| Confidence Limts| 1| 3. 5895| 0. 019262| 5. 3664| 0. 0498| 13. 874| 3. 5895±0. 023948| 2| 3. 6085| 0. 057153| 15. 838| 0. 1975| 54. 731| 3. 6085±0. 040846| The two data differ in all the components, but what’s important are the relative standard deviations and the relative range. The standard deviation and the relative range, along with the confidence limits went up from data set 1 to 2.

This shows that the data became less precise as more values were added, which is normal since one cannot always expect perfect results from every trials. The relative values all show the precision of the data from each other—the lower the number, the more precise they are. However, since the number of elements increased as the relative values increased as well, we can say that data set 1 is more precise but it isn’t accurate, since the sample population is quite limited. Statistical values have been computed and analyzed so that when further, more difficult research arises, the researchers will be able to accomplish them without problems.

These values are significant in determining the accuracy of the experiment. For example in this experiment, the actual weight of 25 centavo coins is found to be 3. 6g for brass plated steel coins minted from 2004. It can be deduced that the majority of the coins used are indeed from that value, and that the mean became more accurate to the true value as more samples were used.

REFERENCES

  1. Silberberg, M. S. (2010). Principles of general chemistry (2nd ed. ). New York, NY: McGraw-Hill Jeffery, G. H. , Bassett, J. , Mendham, J. , & Denney, R. C. (1989).
  2. Vogel’s textbook of quantitative chemical analysis (5th ed. ). Great Britain: Bath Press, Avon http://www. bsp. gov. ph/bspnotes/banknotes_coin. asp. Accessed Nov. 21, 2012.
  3. Appendix Working Calculations Q-test Data Set 1 (Highest) Qexp=|3. 7531-3. 6921|0. 1920=0. 3177 0. 3177<0. 625 (accepted) Data Set 1 (Lowest) Qexp=|3. 5611-3. 6104|0. 1920=0. 2568 0. 2568<0. 625 (accepted)
  4. Data Set 2 (Highest) Qexp=|3. 7531-3. 6921|0. 1938=0. 3148 0. 3148<0. 466 (accepted) Data Set 2 (Lowest) Qexp=|3. 5593-3. 5611|0. 1938=0. 009288 0. 009288<0. 466 (accepted)

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Evaluate the Usefulness of Primary Methodologies

Primary methodologies are ways we gather information when conducting social research. There are multiple types of useful methodologies in collecting qualitative data like interviews and a focus group as well as quantitative data like questionnaires, surveys and statistical research for examples. There are many advantages and disadvantages to all primary methodologies, including the information collected being more personally suited to the researcher while being more time consuming than some secondary research.

One advantage of primary methodologies is the amount of information you can access from people. Some methodologies, like surveys, can generate qualitative data from a large number of participants easily. A survey, which is a ‘systematic snapshot used to infer for a larger whole’ , are easy to administer, are simply created, are cost effective and efficient in collecting information from a large number of respondents . Researchers can reach respondents, nationally and globally, through many means like the Internet and can collect the data in convenience too .

But surveys can become unreliable due to when a survey is poorly written (surveyor bias, poor choice of wording and questions), respondent bias, respondents not answering properly (lack of motivation, afraid of honesty) and a lack of response to the survey . Surveys are an example of a useful primary methodology in collecting qualitative data like statistics from a wide range of people, if written properly and easy to understand. Primary methodologies are useful in collecting personal data fitted to the social research being conducted.

The researcher can choose appropriate methodologies which can best collect the qualitative and quantitative information required. An interview is far more personal than other primary methodologies, like a questionnaire, as the interviewer works directly with the respondent and creates questions based on the participants experience and can also ask follow-up questions, what you can’t achieve in surveys. Data collected from structured interviews can be qualitative and quantitative .

Interviews however can be time consuming for both interviewer and respondent and although it is usually easy for the respondent, especially when asked for an opinion or impression, interviews can be hard to conduct for a researcher . Interviews are useful in creating personal information suited to the research and can have more detailed data than other methodologies. A focus group is an additional primary methodology which can give detailed information, which is another advantage. When people are gathered and asked and presented with specific questions and ideas to create discussion, comprehensive data can be retrieved and used in research.

Group discussions can uncover and explain issues and reactions which may not have been expected or surfaced in a survey or questionnaire. Issues can be examined more in-depth than a general quantitative survey and, like an interview, can include follow-up questions to provide rich and insightful data and feedback . Focus groups on the other hand are also more time consuming than secondary research and can be costly (paying participants to cover travelling and time spent, catering costs, room hire, tape/recording equipment).

Costs for focus groups for some companies in 2010 costed between $4000 and $6000, paying each participant an average of $500. Data from focus groups can’t essentially be used to make a generalisation for the population, due to small numbers being assessed. A focus group of a few hundred people is needed for reliable results, which is cost prohibitive. Skilled moderators can be in addition hard to find . Focus groups while effective in providing detailed information like from interviews has its flaws like all methodologies, even though they are very useful in marketing for example.

Primary methodologies are useful in social research but they all have their disadvantages. Methods like passive or active participant observation have their benefits like being immersed in the research topic but people knowing that they are being observed often change their behaviour to be seen in a more positive light . By taking measures in eliminating bias and receiving accurate and reliable results primary methodologies are are effective tools in research along with secondary research.

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Scientific Method Allows to Uncover Truth

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Hypothesis and Conclusion

Science proceeds by a continuous, incremental process that involves generating hypotheses, collecting evidence, testing hypotheses, reaching evidence-based conclusions. (Michael, 2002). The scientific process typically involves making observations, asking questions, forming hypotheses and testing hypotheses by way of well-structured experiments. Science in Action’s Science Fair Projects & More, 2010-2011). The scientific method is the steps used by many to find answers to questions they want to know. A scientific method is an approach to acquiring knowledge that contains many elements of the methods, and it tries to avoid pitfalls of any individual method used by itself. (Rybarova, 2006). Methods of inquiry are ways in which a person can know things or discover answers to the questions. (Rybarova, 2006). What are the five scientific methods of research inquiry and how they are defined?

Explain how it is applied to the research project and provide examples. Develop a hypothesis focused on the professional practices of criminal justice practitioners. Then select two methods of inquiries and how you would apply them to your hypothesis to reach a conclusion. The five scientific methods of research inquiry are question, hypothesis, experiment, data analysis, and conclusion. The question process is what I want to learn, which in this process you will decide what variables you want to change and how.

Regents of the University of Minnesota, 2003-2012). Ask yourself, is it testable or non-testable? Those variables will be dependent and independent variables. A characteristic whose value may change, vary, or respond when manipulated experimentally is called a dependent variable. (Regents of the University of Minnesota, 2003-2012). Conversely, something that affects the characteristic of interest is called an independent variable. (Regents of the University of Minnesota, 2003-2012). The dependent variable is what you will study. Regents of the University of Minnesota, 2003-2012).

The hypothesis is your thought on why it is or an educated guess. It is a possible explanation that is intended to be tested and critically evaluated. (Rybarova, 2006). Hypotheses clarify the question being addressed in an experiment, help direct the design of the experiment, and help the experimenters maintain their objectivity. (Regents of the University of Minnesota, 2003-2012). You are generating a testable prediction. (Rybarova, 2006). A method is replication or sample size, constant conditions, and control.

Regents of the University of Minnesota, 2003-2012). You are evaluating the prediction by making systematic, planned observation, which involves research and data collection. (Rybarova, 2006). Then, the results, which is describing and understanding the results of an experiment are critical aspects of science. (Regents of the University of Minnesota, 2003-2012). Once you are at this step you can decide if the original hypothesis was true or false. You can use this observation to support refute, or refine the original hypothesis. (Rybarova, 2006).

Finally, the conclusion is the results you got from the research compared to the question. Did your question get the answer it wants, and why or why not. Understanding and applying it to your scientific inquiry will give you a good if not the best chance to arrive at reliable, objective and credible scientific findings. (Science in Action’s Science Fair Projects & More, 2010-2011). My question is has airline safety gone to the extreme since 9/11. This question is testable. My hypothesis or prediction is that airline safety has gone to the extreme since 9/11.

So how will I test this theory? I would do a telephone survey with 500 customers at use at least one of the four major airports. The questions will revolve around the customer’s experience with the airline security and safety issue since 9/11. In an article written by Bill McGee in the USA TODAY stated that “while the Transportation Security Administration’s effectiveness has been hotly debated, there’s no denying that the “hassle factor” of flying commercially has soured many Americans on traveling by air. ” (McGee, 2012).

Although the heightened airport security procedures do not directly affect airline operations, the new process has caused a noticeable subset of airline passengers who opt for different modes of transportation or skip travel entirely. (Logan, 2004). An economic study from Cornell University in 2007 showed that federal baggage screenings brought about a 6 percent reduction in passenger volume across the board, with a 9 percent reduction in the nation’s busiest airports, totaling a nearly $1 billion loss for the airline industry. (Logan, 2004). Has the airline’s safety gone to the extreme since 9/11?

Yes, they have gone to the extreme to most of the passengers who used the airlines. Since they have to change the airline security policy they have lost quite a few passengers. These passengers have chosen to take a different travel alterative. My results have shown that passengers have stopped using the airlines as much, but does not state exactly why they do not use the airlines.

References

  1. Logan, G. (2004). The Effects of 9/11 on the Airline Industry. USA TODAY. http://traveltips. usatoday. com/effects-911-airline-industry-63890.html
  2. McGee, B. (2012). Five most significant changes in air travel since 9/11. USA TODAY. Travel. http://travel. usatoday. com/experts/mcgee/story/2012-06-27/Five-most-significant-changes-in-air-travel-since-911/55841424/1
  3. Michael, R. (2002). Strategies for Educational Inquiry: Inquiry ; Scientific Method. Fall 2002 — Y520: 5982 http://www. indiana. edu/~educy520/sec5982/week_1/inquiry_sci_method02. pdf
  4. Regents of the University of Minnesota. (2003-2012). The Scientific Method. http://www. monarchlab. org/mitc/Resources/StudentResearch/ScientificMethod. aspx
  5. Rybarova, D. (2006).Introduction Acquiring Knowledge, and the Scientific Method. http://www. google. com/url? sa=t;rct=j;q=;esrc=s;frm=1;source=web;cd=9;cad=rja;ved=0CGIQFjAI;url=http%3A%2F%2Fwww. u. arizona. edu%2F~dusana%2Fpsych290Bpresession06%2Fnotes%2FCh1%2520Introduction%2C%2520Inquiry%2C%2520and%2520the%2520Scientific%2520method.ppt;ei=TeA_UaGqD8vZyQHD-4GQAg;usg=AFQjCNEbxy8umFWok015d60lu9H6Y8t0qw.
  6. Science in Action’s Science Fair Projects ; More. (2010-2011). The Scientific Method: The Method in the Madness! http://www. science-fair-projects-and-more. com/scientific-method. html

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