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November 6th, 2015

How to Use Regression Analysis Effectively

So, you want to use regression analysis in your paper? While statistical modeling can add great authority to your paper and to the conclusions you draw, it is also easy to use incorrectly.

The worst case scenario can occur when you think you’ve done everything right and therefore reach a strong conclusion based on an improperly conceived model. This guide presents a series of suggestions and considerations that you should take into account before you decide to use regression analysis in your paper.

The best regression model is based on a strong theoretical foundation that demonstrates not just that A and B are related, but why A and B are related.

How to Use Regression

Before you start, ask yourself two important questions: is your research question a good fit for regression analysis? And, do you have access to good data?

1. Is Your Research Question a Good Fit for Regression Analysis?

This depends on many different factors. Are you trying to explain something that is primarily described by numerical values? This is a key question to ask yourself before you decide to use regression. Although there are various ways to use regression analysis to describe non-numerical outcomes (e.g., dichotomous yes/no or probabilistic outcomes), they become more complicated and you will need to have a much deeper understanding of the underlying principles of regression in order to use them effectively.

Before you start, consider whether or not your dependent variable is numerical. Some examples:

  • Number of years a politician serves in Senate
  • Life expectancy
  • Lifetime earnings
  • Age at birth of first child

At the same time, you need to make sure that there is sufficient variation in your dependent variable and that the variation occurs in a normal pattern.

For example, you would have a problem if you tried to predict the likelihood of someone being elected as president because almost no one is elected as president. As a result, there is virtually no variation on the dependent variable.

2. Do You Have Access to Good Data?

Before you can conduct any type of analysis, you need a good data set. Not all data sets are easily suited to regression analysis without considerable manipulation.

Some things to consider before you decide to use regression:

  • Are most of your independent variables numerical in nature? The best data set for regression will have variables that are primarily described by numbers that vary on a continuous scale. On the other hand, if most of your variables are categorical, you might consider using a different method of analysis (e.g., Chi-squared).
  • Are there enough cases (n) in your data set? Particularly if you think you might use multiple regression, where multiple independent variables are used to predict a single dependent variable, you need to have a sufficient number of cases in your sample to obtain significant results. A general rule of thumb is that you need at least 20 cases per independent variable in your model. So if your model includes 5 independent variables, you need a minimum of 100 cases.

Keep in mind that your independent variables need to meet the same criteria for normality and variability as your dependent variable.

 

Once you decide to proceed with a regression model in your analysis, there are a three key concepts to keep in mind as you design your model to avoid making an easily preventable mistake that could send your conclusions way off track.

  • Parsimony
  • Internal Validity
  • Multicollinearity

Each is described in more detail below.

Parsimony

In statistics, the principle of parsimony is based on the idea that when possible, the simplest model with the fewest independent variables should be used when a model with more variables offers only slightly more explanatory value. In other words, one should not add variables to a model that do not increase the ability of the model to explain something.

Only add variables to a model if they significantly increase the ability of the model to explain something.

If you add too many variables to your model, you can unwittingly introduce major problems to your analysis.

In the extreme case, you must consider that your R2 value will always increase with the addition of new variables: so if you examine R2 alone, you can be duped into thinking that you have a great model simply by dumping in more and more predictor variables.

There are two good ways to address this problem: use an Adjusted R2 to compare models with different numbers of predictors, and use stepwise regression to analyze the explanatory impact of each variable as it is added to the model.

  • Adjusted R2 takes into consideration the number of variables used in the model, and only increases when the addition of a new variable explains more than would random chance alone. So although a model with 10 variables might have a very high R2 value, the Adjusted R2 could actually be much lower than a model with fewer variables. Selecting your model based on Adjusted R2 helps you select a more parsimonious model that is less likely to have other problems (e.g., see multicollinearity below).
  • Stepwise Regression is a computational method of assessing the additional explanatory value of each variable as they are added to the model in different orders. It can be used to parse out superfluous variables from a model, however it needs to be used carefully and in concert with theoretical guidance to avoid overfitting your data.

A good rule of thumb as you consider different models is that you should always have a good reason to add a predictor variable to your model, and if you can’t come up with a good theoretical explanation as to why A influences B, then leave out A!

Internal Validity

Internal validity is the degree to which one factor can be said to cause another factor based on three basic criteria:

  1. Temporal precedence, i.e., the “cause” precedes the “effect.”
  2. Covariation, i.e., the “cause” and “effect” are demonstrably related.
  3. Nonspuriousness, i.e., there are no plausible alternative explanations for the observed covariation caused by a confounding variable.

In many cases, internal validity becomes an issue in the form of a “chicken and egg” problem.

For example, let’s say you are considering the relationship between obesity and depression (a common example). If you want to include depression as an independent variable to explain obesity in your model, you first need to consider the question:

Does depression lead to obesity, or does obesity lead to depression?

If you have no clear theoretical guidance to show that, in fact, depression usually precedes obesity (temporal precedence), you could introduce a significant problem to your model if the relationship is in fact the other way around: depression being the result of obesity.

Therefore, as you craft your model it is important to have a theoretical basis for the inclusion of each variable.

Multicollinearity

Multicollinearity occurs when the independent variables in a multiple regression model are highly correlated with one another. This can be a problem in several ways:

  • It reduces the parsimony of your model if the two variables are highly similar (e.g., two different variables that effectively measure the same thing);
  • Multicollinearity can lead to erratic changes in the coefficients (measured effect) of predictor variables;
  • As a result, it can be difficult to interpret the results of a model with high multicollinearity among predictors. Specifically, it becomes impossible to discern the individual effect of different regressors.

An example of variables that are going to be highly multicollinear are any variables that effectively measure the same thing. One way to show this, for the purposes of an example, is to imagine converting categorical data into a series of binary variables.

Any variables that effectively measure the same concept are likely to have high collinearity.

For example, let’s say that we have a variable measuring memory where respondents are able to choose very good, average, or poor as a response.

One way to use this data in a regression model would be to convert the data into three dichotomous (yes/no) variables indicating a person’s response.

However, if you then include all of these dichotomous variables in your model, you will have a big problem because they will become perfectly multicollinear. This is because anyone who indicated that they had a very good memory, by default, also indicated that they do not have a poor memory. The two variables measure the same thing: a person’s memory.

Another common example can be found in the use of height and weight variables. Although the two variables measure different things, broadly speaking they can both be said to measure a person’s body size, and they will almost always be highly correlated.

As a result, if both variables are included as predictors in a model, it can be difficult to discern the effect that each variable has individually on the outcome (measured by the coefficient).

Thus, as you build your model, you need to be aware of the potentially confounding impact of using highly similar predictor variables. In an ideal model, all independent variables will have no or very low correlation to each other, but a high correlation with the dependent variable.

 

Conclusion: Use Regression Effectively by Keeping it Simple

Regression analysis can be a powerful explanatory tool and a highly persuasive way of demonstrating relationships between complex phenomena, but it is also easy to misuse if you are not an expert statistician.

If you decide to use regression analysis, you shouldn’t ask it to do too much: don’t force your data to explain something that you otherwise can’t explain!

Moreover, regression should only be used where it is appropriate and when their is sufficient quantity and quality of data to give the analysis meaning beyond your sample. If you can’t generalize beyond your sample, you really haven’t explained anything at all.

Lastly, always keep in mind that the best regression model is based on a strong theoretical foundation that demonstrates not just that A and B are related, but why A and B are related.

If you keep all of these things in mind, you will be on your way to crafting a powerful and persuasive argument.

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March 30th, 2015

How to Manage a Group Project (Video)

Group work is an inevitable part of most university courses and the ability to work well with other people is something all employers care about. While working on a group project can be incredibly rewarding, it can also present real challenges if you don’t go in with the right mindset. Here are a few tips to make group work just a little bit easier!

Be Prepared to Compromise

Something we must learn early in life is that different people have different working styles. While some people like to have an essay planned out and written weeks in advance, others thrive on the pressure of leaving it until the last minute. Be open about how you work from the start – if you talk about the ways in which each person works best right away, you can come up with a compromise that suits everyone.

If everyone compromises a little – for example, by agreeing to pre-planned deadlines – this can help avoid leaving some group members stressed or upset by discovering that their expectations were out of line with the rest of the group.

 

Maximize Each Member’s Strengths

Do you love public speaking? If so, great – tell your group members that from the start! Break down everything that has to be done, from conducting the research to preparing the slideshow and giving the presentation in front of the class, and assign tasks to each person based on their strengths.

While it can be difficult to please everyone, having an honest discussion about strengths/weaknesses early on and and attempting to give everyone tasks that they’re comfortable with will benefit the entire group in the end.

 

Stand Up for Yourself and Do the Work

People have different personalities, so if you are naturally shy and are put in a group with someone more confident, it can be tempting to shrink up and not say or do anything, even when you think that the group might be headed in the wrong direction – this is a mistake!

As scary as it is, make sure you stand up for yourself and speak up. This is the only effective antidote to groupthink and conversations where not everyone immediately agrees can be incredibly fruitful.

Of course it goes without saying, always put in the work. Don’t be the person that shows up with the job half done. It is common for group projects to include peer assessments and if you don’t put in the effort, your classmates won’t be shy.

 

Choose Your Group Wisely

If you are given the opportunity to choose your group members, the temptation is often to work with your friends. Sometimes that is for the best because you know each other well and it can make working on the project more fun and less stressful. However, it can also lead to even more tension, particularly if you aren’t diligent about assigning tasks and preparing some deadlines from the get go.

Someone who you have a lot of fun with on a night out might not make the best partner for a group project. (For one thing, this can make it much easier to get distracted!)

There are also a lot of benefits to working with people you don’t know – it can give your project a wider range of perspectives and help you capitalize on differentiated skills as a group. Moreover, you might even end up making a great new friend.

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March 23rd, 2015

Presentation Tips 101 (Video)

Presentations have become an integral part of most university and college courses. While some students won’t think twice before getting up to speak in front of a room full of people, for others, the thought of being in the spotlight can become overwhelming. It’s natural to be nervous, but for many students, those nerves can spiral out of control, making you feel anxious for days leading up to the event.

Here are a few tips which will hopefully help to make you feel as comfortable as possible before giving your next group or solo presentation!

Perfect Your Slides

If you are required to make a visual background for your presentation on something like PowerPoint, make a really good job of it! Rather than cobbling together some blank slides with a couple of paragraphs on them the night before, take some time to make them look amazing!

A well-structured, nicely designed slideshow will show your teacher and classmates that you put a lot of work into the presentation. This tells your audience that any visible nerves are purely due to public speaking and not from a lack of preparation.

Having your key points outlined briefly on your slides also means that if your nerves get the better of you and you lose track of where you are, your slides will quickly guide you back to where you were.

 

Practice, Practice, Practice!

It sounds obvious, but the worst thing you can do if public speaking worries you is not run through your presentation a good few times in advance! Start off alone, speaking aloud in your bedroom or an empty classroom. Then ask some friends to act as a test audience for you.

Not only will this likely lead to useful feedback on your content, but it will make you feel more comfortable in front of a crowd, too! It allows you to practice key strategies — such as eye contact — which will improve your presentation. Your tutor wants to see that you are engaging with the class, so getting used to being in front of others is really helpful.

 

Make Use of Note Cards

Note cards can be a useful tool to take advantage of, but do make sure you check that you are allowed to use them first! Having cards with brief summaries (not the full script of your presentation) can help to keep you on track and, much like the slideshow, can give you the confidence of knowing exactly what’s coming next.

However, they can also be a useful tool to stop you from fidgeting, something which is ever so tempting when you’re nervous! If you have cards to hold, you won’t be as likely to touch your hair, fidget with a pen or fiddle with your jacket!

 

Plan Something Nice for Later!

Depending on your schedule, if you can afford to take a little time out to go out for dinner with friends, go to the cinema, or even just go for a walk round the shops – do it! Knowing you have something fun planned for after the big event can make it so much easier to get through the stress of a presentation. You might still be nervous, but knowing that no matter what, the rest of your day is only going to get better, is a great feeling! That alone might be enough to make you feel more settled.

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