Why ANOVA and Linear Regression Are the Same Analysis

If your graduate statistical training was anything like mine, you learned ANOVA in one class and Linear Regression in another. My professors would often say things like "ANOVA is just a special case of Regression," then do a lot of hand waving when pressed to explain.

It was not until I started consulting that I realized how closely related ANOVA and regression are. They're not only related, they're the same thing. Not a quarter and a nickel--different sides of the same coin.

So here is a very simple example that shows why. When someone showed me this, a light bulb went on, even though I already knew both ANOVA and mulitple linear regression quite well (and already had my masters in statistics!). I believe that understanding this little concept has been key to my understanding the general linear model as a whole--its applications are far reaching.

Why ANOVA and Linear Regression Are the Same Analysis

As an example, I use a model with a single categorical independent variable--employment category--with 3 categories: managerial, clerical, and custodial. The dependent variable is Previous Experience in months. (This data set is employment.sav, one of the data sets that comes free with SPSS).

We can run this as either an ANOVA or a regression. In the ANOVA, the categorical variable is effect coded, which means that each category's mean is compared to the grand mean. In the regression, the categorical variable is dummy coded**, which means that each category's intercept is compared to the reference group's intercept. Since the intercept is defined as the mean value when all other predictors = 0, and there are no other predictors, the three intercepts are just means.

In both analyses, Job Category has an F=69.192, with a p Clerical: 85.039
Custodial: 298.111
Manager: 77.619

In the Regression, we find these coefficients:

Intercept: 77.619
Clerical: 7.420
Custodial: 220.492

The intercept is simply the mean of the reference group, Managers. The coefficients for the other two groups are the differences in the mean between the reference group and the other groups.

You'll notice, for example, that the regression coefficient for Clerical is the difference between the mean for Clerical, 85.039, and the Intercept, or mean for Manager (85.039 - 77.619 = 7.420). The same works for Custodial.

So an ANOVA reports each mean and a p-value that says at least two are significantly different. A regression reports only one mean (as an intercept), and the differences between that one and all other means, but the p-values evaluate those specific comparisons.

It's all the same model, the same information, but presented in different ways. Understand what the model tells you in each way, and you are empowered.

I suggest you try this little exercise with any data set, then add in a second categorical variable, first without, then with an interaction. Go through the means and the regression coefficients and see how they add up.

**The dummy coding creates two 1/0 variables: Clerical = 1 for the clerical category, 0 otherwise; Custodial = 1 for the custodial category, 0 otherwise. Observations in the Managerial category have a 0 value on both of these variables, and this is known as the reference group.

Why ANOVA and Linear Regression Are the Same Analysis
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© 2008 Karen Grace-Martin -- Statistical Consultant and founder of The Analysis Factor

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Selling Your Home Yourself in Six Steps: You Can Do It!

Contrary to what 99 out of 100 agents will tell you, it IS possible to sell your home yourself. When you undertake that task, you'll become a FSBO (pronounced "fisbo," and short for "for sale by owner"), and though it can be a challenge, it's one that thousands of home sellers tackle every day. And you can do it, too! In a nutshell, here are the things to do to become a successful FSBO.

Clean your home (inside and out) and get the yard looking spic-and-span. Set a sales price based on selling prices of homes nearby of similar size and amenities. Put a FSBO sign in your front yard with your phone number and/or email address.Place an ad in the real estate classified section of your local paper. Pass out flyers to your neighbors and put at your local shopping mall, stores, libraries, and apartment complexes.Hold an open house.

Now let's look at them individually. Cleaning up and doing whatever maintenance seems self-explanatory, but be aware that you get used to certain things (especially odors) when you live in a home everyday. So it's worthwhile to ask someone to walk through your house and give you an honest appraisal of things that need to be fixed or smells that need to be addressed, such as sticky doors, squeaky hinges, and the cat box in the utility room.

Selling Your Home Yourself in Six Steps: You Can Do It!

Setting a price can be a bit tricky, but you can find out what other homes are on the market by calling the agents listed on signs in your neighborhood and asking the prices of their houses. If the homes have been on the market a long time, you can assume they're over priced.

Putting a sign in your yard is easy. They're available in most hardware or department store, and they're cheap. Yet most agents will tell you that signs are the best advertising mediums, since people who see yard signs are cruising the neighborhood. That means they're in the market for a home in that area, so if you put a sign out, you'll get calls.

Now a word for those who are squeamish about putting your phone number on a sign. You can substitute an email address to protect yourself from unwanted calls. It will limit your number of prospects, but it will give you a greater degree of privacy. Since you're moving anyway, it might be best to list your phone number. If you know how to put pictures on the Internet, you can list you website address on the sign.

Placing a newspaper ad is easy, but make sure to give accurate information and make it enticing. Be brief, but tell buyers what's special about your home. Even with the advent of the Internet, a majority of homebuyers still cruise neighborhoods and religiously peruse real estate ads, especially on Sundays.

Putting up flyers in the area will also let people know your home is available. This can be especially effective for apartment dwellers longing to own a home of their own.

Open Houses

Handing out flyers to neighbors and inviting them to an open house can be your most effective selling tool. After all, your neighbors are happy living in your area and often have friends or family they'd love to have closer to them.

You'll notice I didn't suggest holding an open house and inviting the world. The type of open houses you see agents promoting are for the agents to get leads on home buyers. Few houses sell at open houses.

There are other factors to consider after you've found a buyer, but you can generally find help through a lawyer or an escrow company. The bottom line is: you CAN sell your home yourself. It just takes time, diligence, and attention to detail.

Copyright © 2006 Jeanette J. Fisher

Selling Your Home Yourself in Six Steps: You Can Do It!
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Teleseminars - How To Use Articles and Teleseminars To Boost Your Business On The Internet

Teleseminars are calls that give you an opportunity to present your information and expertise to others from the comfort of your telephone. People can call in from anywhere in the world to hear what you have to teach to them.

Your listeners will call in on something called a bridge line. There are some bridge lines that are free, while others charge a small monthly fee for access. The most convenient times to offer teleseminars are usually Tuesday, Wednesday and Thursday, from about four o'clock in the afternoon until eight o'clock. Depending on your topic and your listeners you may be able to give calls during the day. This would work well for people who are at home during the day, or for those who work from their homes.

I learned the concept of giving teleseminars from Jeff Herring. Jeff offers a free call each week, where he introduces his topic of article writing and marketing to promote business on the internet. From these free weekly calls he is able to get many people to sign up for teleseminars that will be given over a four week period or longer. These are paid teleseminars and teach the listeners much more than the weekly calls do.

Teleseminars - How To Use Articles and Teleseminars To Boost Your Business On The Internet

Teleseminars can also be transcribed and turned into eBooks that can be sold from a website or from a blog. If you have information that you want to pass on to others, writing articles and giving teleseminars can be an excellent way to do it.

Teleseminars - How To Use Articles and Teleseminars To Boost Your Business On The Internet
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TeleSeminar Profit Systems - Read This When You are Ready to Use TeleSeminars to Accelerate Your Biz

Growing your internet business is a challenge for any one. It takes time, skill and knowledge, and you have many competitors in your niche.

One of the strategies I have found to grow my internet business is to use teleseminars.

Here are some tips you can use right away to accelerate the growth of your business with teleseminars.

TeleSeminar Profit Systems - Read This When You are Ready to Use TeleSeminars to Accelerate Your Biz

Tip 1 - Reach more people at one time - When you are on the phone speaking to a group of people, you have left the old model of one to one far behind. You are now able to reach, at one time, as many people as you are able to get on the phone. These people are hearing your voice instead of just reading your words, and they will come to know, like and trust you much more rapidly.

Tip  2 - Write articles with your voice - Hold a teleseminar, record it and have it transcribed. You can easily get eight to ten great articles from the transcription of a sixty minute teleseminar.

Tip 3 - Create e-books with your voice - In the same way you can write articles with your voice, you can create an ebook with your voice as well. Hold your teleseminar, record it and have it transcribed. With just a little bit of tweaking, you can convert  the transcript into an ebook.

While there are many other ways you can use this strategy to accelerate your internet business, if you just use these three, you will have taken powerful steps to accelerate your business with teleseminars.

TeleSeminar Profit Systems - Read This When You are Ready to Use TeleSeminars to Accelerate Your Biz
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From Jeff Herring - The Article Guy & Great Article Marketing

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Top Ten Fonts for Website Design

The top ten fonts for website design might change in order, but for the most part the fonts that make up this list stay the same due to their popularity. In general, the top ten list includes Arial, Frutiger, Futura, Gills Sans, Helvetica, Lucida, Optima, Palatino, Agfa Rotis, and Univers.

The reason these fonts are so popular is because they are simple and easy to read on computer screens with low resolution. As a result, most of the time fonts that are unique, wild, and distinctive are not used on web pages so as not to distract the reader from what is trying to be said and communicated through the font on the page. Since the website uses content to get the point across, it is prudent to use fonts that are easy to read. If you make it difficult for a visitor to read the content, they will more likely leave than put forth the effort. Consider the following points as well when developing your fonts for your website.

Web Hosting

- Big Fonts

Top Ten Fonts for Website Design

This is your web page and likely your livelihood, not a term paper or research project that has a defined style. Because of this, you can use big fonts, bold them, make them stick out and attract the reader. You can drive your point home with larger fonts and they also will be significantly easier for your visitor to read. The object of your website is to present information that is easily seen, read, and found by visitors. So, go ahead and increase the font size even in regular text that is not in a heading or title. Many of your visitors will thank you because they will not have to put on their glasses or strain to read the text. Sometimes bigger is better.

- Sans Serif

If you have no idea about fonts, how they translate to your web page, or how they will affect your visitors and ultimately sales, then you should definitely stick with a san serif font. The reason for this is that these fonts are the most legible and provide the best readability for visitors in a low resolution atmosphere. Don't take risks with your fonts, go generic and use a sans serif font. Your visitors will thank you for it and your sales will not suffer from it.

- Simple is Safe

Again, don't let yourself get carried away with your fonts and designs. Instead, keep the thought in mind that simple is safe. If you want to be bold and brazen in your website design then don't take that route with your fonts. Keep it simple, basic, and easy to read, and you will benefit significantly more than if you try to mix it up.

Top Ten Fonts for Website Design

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