Typically, when a researcher wants to determine the linear relationship between the target and one or more predictors, the one test that would occur to the researcher is the linear regression model. 

Linear regression attempts to analyse whether one or more predictor variables explain the dependent variables. While one variable is considered to be explanatory, the other is deemed to be a dependent variable. The linear regression line represented by, Y = a + bX, where ‘Y’ is the dependent variable, ‘X’ is an explanatory variable, ‘a’ is the intercept and ‘b’ is the slope.

For instance, a researcher would want to relate the heights of individuals to their weights using this test. Prior to trying to fit a linear model to observed data, the researcher must investigate whether there is a relationship between the interested variables. To determine this, a scatterplot is used. If no association between the explanatory and dependent variables exists, then fitting a linear regression model to the data will not deliver a useful model. 
The numerical measure of association between two variables is known as the correlation coefficient, and the value lies between -1 and 1. 

The linear regression test has five key assumptions

1. Linearity relationship between independent & dependent variable
   
2. Statistical independence of errors (no correlation between consecutive errors particular in time series data)
   
3. Homoscedasticity of errors
   
4. Normality of error distribution
   
5. No or little multicollinearity 
   

If any of these assumptions are violated, then the scientific insights, forecasts yielded may be inefficient or biased/misleading. Therefore, it becomes a mandate to diagnose the assumptions and find the right solution. 

• Violations of linearity 
  

Diagnosis - Non-linearity is evident in the plot of residuals vs predicted values or observed vs predicted values. The points must be symmetrically distributed around a horizontal line in the former plot, whereas in the latter plot it must be distributed around a diagonal line. This is followed by careful investigation for evidence of a ‘bowed’ pattern, implying that during large or small predictions, the model makes systematic errors. 

Solution - The best way to fix the violated assumption is incorporating a nonlinear transformation to the dependent and/or independent variables. For example, if the data is positive, you can consider the log transformation as an option. Applying a log transformation to the dependent variable is equivalent to an assumption of growing or decaying of the dependent variable exponentially as a function of the independent variables. Applying it to the dependent as well as the independent variables is equivalent to an assumption that the impact of the independent variables are multiplicative and not additive in their original units. This indicates that a small percentage change in any one of the independent variables results in proportional percentage change in the desired value of the dependent variable.

• Violation of independence 
  

Diagnosis - Investigate residual time series plot (residuals vs row number) and a residual autocorrelations. Residual autocorrelations must fall within the 95% confidence bands around zero ( i.e., nearest plus-or-minus values to zero). Look for significant correlations at the first lags and in the vicinity of the seasonal period as they are fixable. 

Solution - You can add lags of the dependent variable and/or lags of the independent variables. Alternatively, if you have an ARIMA+regressor procedure, add an AR(1) or MA(1) to the regression model. While an AR(1) adds a lag of the dependent variable, an MA(1) term adds a lag of the forecast error. If there is seasonality in the model, it can be managed by various ways: (i) seasonally adjust the variables or (ii) include seasonal dummy variables to the model. 

• Violation of homoscedasticity
  

Diagnosis - Investigate residuals vs predicted values plot and in case of time series data, look at residuals vs time plot. Due to the imprecision in the coefficient estimates, the errors tend to be larger for forecasts associated with predictions. Therefore, develop plots of residuals vs independent variables and check for consistency. 

Solutions - If the dependent variable is positive and the residual vs predicted plot represents that the size of the errors is directly proportional to the size of the predictions, a log transformation is applied to the dependent variable. If it has already been applied, then the additive seasonal adjustment is used (similar to linearity assumptions). 
 

• Violation of normality 
  

Diagnosis - The best to check normally distributed errors is by using a normal probability plot. This is a fractiles of error distribution vs the fractiles of a normal distribution plot. If the distribution is normal, then the points on the plot will be close to the diagonal reference line. An S-shaped pattern of deviations determines that either there are too many or two few large errors in both directions. On the other hand, a bow-shaped pattern of deviations indicates that the residual has excessive errors in one direction. 

Solutions - The best solution is the utilisation of nonlinear transformation of variables. An example of nonlinear transformation is log transformation. However, this solution is only used if the errors are not normally distributed. 

• Violations of multicollinearity 
  

Diagnosis - To determine the correlation effect among variables, use a scatter plot. Alternatively, you can also use VIF factor. VIF value of >= 10 indicates serious multicollinearity. On the other hand, if the value <= 4 implies there is no multicollinearity. 

Solution - The best way to eliminate multicollinearity is to remove one of VIF (out of two) from the model. You can use stepwise regression or best subsets regression to remove VIF. If not use Partial Least Square regression (PLS) to cut down the number of predictors. 

By leveraging the solutions mentioned above, fix the violations, control & modify the analysis and explore the true potential of the linear regression model. 

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International supervisors for PhD students can be present as both, a boon as well as a disadvantage. PhD candidates, who are pursuing their degree from a university that boasts of a number of International faculties, may get this International staff as their PhD guides and supervisors.
The role of a PhD Supervisor is extremely substantial for a streamlined process of thesis writing as well as achieving ultimate success by drafting a well written, well researched and good quality thesis. This makes it a prerequisite for any PhD aspirant to maintain harmonious relations with their supervisors.
However, various issues arise when we consider International PhD Supervisors in specific:

1. Language Barriers: A prerequisite in maintaining any kind of relations is the act of communication. However, due to a difference in the first language spoken by both the student and the supervisor, effective communication itself becomes difficult to achieve. This gap between the two might lead to a gradual decline in the interaction between them which raises serious concerns.
   
2. Difference in delegation of authority: In every culture and nationality the role of a PhD supervisor varies. While in India his role is more pronounced and authoritative, in countries such as Australia which have a more Westernised culture, the role of a supervisor is restricted to that of a guide. Decision making in this case lies completely in the purview of the student himself. This contrast might lead to a confusing state of affairs where the student expects the supervisor to make decisions and the supervisor does not wish to be relied upon so much. 
3. Difference in writing styles: The activity of Thesis writing has different dimensions in every nationality. The writing styles, structure of the thesis, formatting style, methods and techniques deployed are all varied. Since all these aspects are essential to any thesis, disagreements regarding them are bound to result into a conflicting circumstance.
   
4. Psychological Gap: Due to the striking difference in the nationality of a PhD candidate and his supervisor, a psychological gap between the two may prevail, where they both do not wish to communicate to avoid any misinterpretations and disagreements.
   

In such cases, the most effective resolution is to adapt to the following:

1. Take the difference in your stride: Make this your competitive advantage over other PhD aspirants. The fact that your supervisor belongs to a different country altogether, implies that he also brings with him a vast body of knowledge specific to his field and country that is unexplored as yet. Talk about the practice of thesis writing adopted in his native country. This would also help in reducing any potential or prevalent psychological gap between the two of you.
   
2. Communicate: The more you communicate with your supervisor, the lesser differences you will realise. This will help you in being frank and open with him, which will ultimately lead to a much more pleasant thesis writing experience. You also need to realise that certain conflicts are bound to arise with your supervisor, irrespective of his and your nationality. Take these supportively and achieve conclusive success.

While writing your dissertation, it is essential to refer books, journals and research work done by different authors, but your work should be unique and not a copy. It is essential to keep your work original and ethical to secure good grade and have a good reputation in the academic world. Here are three tips on how to avoid plagiarism in your dissertation.

Express Your Thoughts​

Select good reference books by authors who have extensively worked on the subject, read and understand the concept before you start writing your dissertation. You cannot get away from plagiarism by merely rephrasing the sentences and claiming it your work. Moreover, when you rephrase, there is a risk of misrepresentation of the concept. Thus, the best way to avoid plagiarism is to grasp the idea and summarize in your words.

Maintain a Bibliography

The bibliography is the list of books and other scholarly articles referred while writing any assignment. While you are collecting the material for your dissertation, remember to collect the name of books along with details like author, year of publication, chapter number or chapter name as well as title of the article. Different institutes have different standards for maintaining the bibliography, read properly the instruction before you start writing.

Quotation and Citation of Others Work

If you have to use the exact word of another author or even your own work, use quotation marks. While quoting, make sure to use the exact same words and give the due credit to the author by citing the source as specified by your institution. Try to avoid quoting too many sentences, it is best to keep the quotes within 40 words. As many evaluators don't prefer quotation.

Apart from these indigenous methods you can check your content for originality from the online plagiarism checker like http://smallseotools.com/plagiarism-checker/  or use paid service a complete package from plagiarismremoval.in/ and many more.

The key to writing an effective dissertation is to demonstrate a comprehensive knowledge of the chosen topics, make a list of your research notes and start writing. You may come across major portions that might require further research, so be ready to revisit the library. The focal point is to maintain a lucid style of writing that can effectively communicate your ideas. Remember, a well-researched and elaborately planned dissertation can be marred by unclear phrasing and poorly expressed ideas.

Focus on the key points for writing a potential thesis.

Find your own Style

Seek an impactful style of writing by researching a number of scholarly articles and pick up the one which is easy to read and understand. Follow the structure, study through the arguments and garner examples of punctuation and vocabulary. Use subheadings in between and tweak the content for readers’ better understanding. Most importantly, avoid repetition and be straightforward in expressing your views.

Structure sentences properly

Distinguish the more important key points than the lesser ones. Highlight the key points by adding sentences that are not too long and difficult to understand. Keep the sentences short, simple, and yet they are potent to present the meaning that your want to convey in to the readers.

Acknowledge Ideas

Yes, a dissertation should contain your original thought, but do refer ideas of others to make your statement more emphatic and reliable. You can use work of others to leverage your arguments, but add a footnote to indicate the original source of the idea as well.

Write Introduction later

Once you reach the conclusion part of your thesis you have an idea of the arguments and the points you made in your research. This will help you write the ‘Introduction’ once you reach the last stage of work.

The Perfect Bibliography

Mention the articles, books, interviews, newspapers, train timetables, cave paintings, statistics that were used as primary sources. In addition to it, do quote secondary sources as well.
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Thus, make it an error-free and perfect study proposal by following the above points.  

Writing a dissertation can be extremely difficult for those students, who do not have the habit of clearly penning their thoughts on paper. However, you cannot get through university without writing a research work of some sort. It is important to hone your writing skills, especially when you have to write a dissertation as a requirement for a postgraduate degree. Here is how you can eliminate the pain from the dissertation writing process.

Select an original topic

Think of an original and a viable topic that covers your specific field of study. This is how the process of writing a dissertation begins. Once your topic has been approved, it implies that you would have to go ahead with writing the dissertation. The main reason why writing a dissertation is important is because you should either be able to get a degree and a job after it or you should be able to study further after obtaining your degree.

Hone your writing skills

Many of the writers of dissertations find it difficult to complete their research because of their poor writing skills. However, it is not necessary that everyone needs to be a literary genius in order to come up with a decent dissertation these days. All you need to do is to put in some efforts and time to come up with an initial draft of the dissertation.

Make notations

While writing your dissertation, make sure you make notations in your research work. Once you are certain that you have gathered enough research materials, you can begin writing your initial draft of the dissertation. You could make up the initial draft based on the materials you have already gathered. After this, you will have a basic idea of what needs to be done for the rest of the dissertation. If you do not have enough materials to go ahead and write the dissertation, then you should consider collecting them and completing your dissertation.

It takes a lot of meticulous planning and time to write one’s dissertation. Many students do not even have an idea of how to write their dissertations and end up writing dissertations that are of a very poor quality. Here are certain tips on improving your dissertation writing style. 

No matter what you do, you should develop an interest in it. You should not write such that it would give your reader an impression that you wrote the dissertation for the sake of writing it. Interest is a major factor that reflects in your writing. When you do the task with interest, it is likely to become an enjoyable one. 

Choose a Title

It is important to select a title that will give your readers a basic idea of what the research is on. It should be so attractive that it would automatically grab a few eyeballs. You should, however, remember that the title you have selected should neither be too long nor too short, but just right.

Length

You need to have an in depth knowledge of the topic you have undertaken for your study. It should align with the topic of your interest. Do not add details that are unnecessary for the sake of making it long. The dissertation should be written in such a way that your supervisor understands it easily. It should reflect on your competence.

Error free copy

You should make sure that your dissertation does not have any kind of errors. It should be free of punctuation and grammatical errors. A dissertation that has been written poorly will make a bad impression on your supervisor. This would result in a loss of marks. If you make too many mistakes, it can result in a poor quality or a weakly presented dissertation. 

A literature review is a thorough summary of your dissertation as well as a study of the original research done on the subject you have chosen. It is a highly objective and critical analysis of the available research literature on the topic that is being researched on. Here is how you have to write an effective literature review for your dissertation proposal.

Select a Good Topic

It can be a daunting task to select a good topic for your literature review. A common error by those who are novice reviewers is that they select a review title that is all encompassing. Even though this may be an initially useful strategy, this much literature would eventually make the literature review impractical at the end of the day. It is, therefore, advisable to not use too many books in the literature review. For instance, you would need to concentrate on the amount of information that is truly necessary in order to make the data you have gathered manageable. Identifying what is of interest to you will help you narrow down or refine the literature.

Search the Literature

After you have selected the topic, it is important to search for literature. You should define the type of source while searching for the literature. While searching for literature, you should also mention the keywords with which you did the search.

Synthesize the Literature

When you have finished collecting the literature, you should consider analyzing and synthesizing it. You should learn to summarize the literature you have collected and review them in a paragraph of three hundred to five hundred words. You must then structure the review and then write it accordingly. The key to writing a good literature review is the ability to present it very well. Write your own reaction to each piece that you are reviewing. Reactions include those things that strike you as being particularly useful.

Transitory years have changed a lot in the process and presentation of PhD. It has become much more specific and task ridden within a decade. Thus the illusion of research scholars regarding their blasé PhD falls on a drowning trail. At present, if you want to score good marks and gain knowledge in your doctorate journey, you have to be proactive and diligent too. Undoubtedly, a good PhD thesis requires comprehensive theoretical content, real and firsthand data’s, an allied research methodology and interpretation of result in the conclusion. You being meticulous and professional can frame your thesis by following all the above contexts very well. Your task can become even easier if you may follow underneath mentioned points-

• Go through your institutional demands – As finally your thesis has to go in hand of your institution or university  professors and they will definitely follow the guidelines as suggested to them, so going against them or ignoring these guidelines would be an imprudent act. 
  

• Planning – Framing an outline regarding the arrangement of text and chapters to be included will complete your 50% of the work. You can also take help of your mentors in deciding the structure of your thesis. 
  

• Organizing – Laying down your collected information’s and data’s according to the planned structure of the thesis will give a synchronized look to your thesis. Include all your notes, paper works done during your researching period, data’s you have collected and any extra guideline suggested by your guide in respect of your topic while you are compiling the contents. Also, don’t leave any stone unturned; explain and exemplify each and every point mentioned in the thesis, as leaving an isolated content can give a blank impression about you and your thesis.
  

• Check and re-check – Never forget to submit your thesis without checking and revising it as any blunder left uncorrected will let down your entire effort. 

Furthermore, your consciousness towards your research right from the beginning can no longer stop you in writing a good PhD thesis.