Posts Tagged ‘Bureau of the Census’

Forecast Friday Topic: Heteroscedasticity

August 12, 2010

(Seventeenth in a series)

Recall that one of the important assumptions in regression analysis is that a regression equation exhibit homoscedasticity: the condition that the error terms have a constant variance. Today we discuss heteroscedasticity, the violation of that assumption.

Heteroscedasticity, like autocorrelation and multicollinearity, results in inefficient parameter estimates. The standard errors of the parameter estimates tend to be biased, which means that the t-ratios and confidence intervals calculated around the suspect independent variable will not be valid, and will generate dubious predictions.

Heteroscedasticity occurs mostly in cross-sectional, as opposed to time series, data and mostly in large data sets. When data sets are large, the range of values for an independent variable can be quite wide. This is especially the case in data where income or other measures of wealth are used as independent variables. Persons with low income have few options about how to spend their money while persons with high incomes have many options. If you were trying to predict that the conviction rate for crimes was different in low income counties vs. high income counties, your model may exhibit heteroscedasticity because a low-income person may not have the funds for an adequate defense, and may be restricted to a public defender, or other inexpensive attorney. A wealthy individual, on the other hand, can hire the very best defense lawyer money could buy; or he could choose an inexpensive lawyer, or even the public defender. The wealthy individual may even be able to make restitution in lieu of a conviction.

How does this disparity affect your model? Recall from our earlier discussions on regression analysis that the least-squares method places more weight on extreme values. When outliers exist in data, they generate large residuals that get scattered out from those of the remaining observations. While heteroscedastic error terms will still have a mean of zero, their variance is greatly out of whack, resulting in inefficient parameter estimates.

In today’s Forecast Friday post, we will look at a data set for a regional housing market, perform a regression, and show how to detect heteroscedasticity visually.

Heteroscedasticity in the Housing Market

The best depiction of heteroscedasticity comes from my college econometrics textbook, Introducing Econometrics, by William S. Brown. In the chapter on heteroscedasticity, Brown provides a data set of housing statistics from the 1980 Census for Pierce County, Washington, which I am going to use for our model. The housing market is certainly one market where heteroscedasticity is deeply entrenched, since there is a dramatic range for both incomes and home market values. In our data set, we have 59 census tracts within Pierce County. Our independent variable is the median family income for the census tract; our dependent variable is the OwnRatio – the ratio of the number of families who own their homes to the number of families who rent. Our data set is as follows:

Housing Data

Tract

Income

Ownratio

601

$24,909

7.220

602

$11,875

1.094

603

$19,308

3.587

604

$20,375

5.279

605

$20,132

3.508

606

$15,351

0.789

607

$14,821

1.837

608

$18,816

5.150

609

$19,179

2.201

609

$21,434

1.932

610

$15,075

0.919

611

$15,634

1.898

612

$12,307

1.584

613

$10,063

0.901

614

$5,090

0.128

615

$8,110

0.059

616

$4,399

0.022

616

$5,411

0.172

617

$9,541

0.916

618

$13,095

1.265

619

$11,638

1.019

620

$12,711

1.698

621

$12,839

2.188

623

$15,202

2.850

624

$15,932

3.049

625

$14,178

2.307

626

$12,244

0.873

627

$10,391

0.410

628

$13,934

1.151

629

$14,201

1.274

630

$15,784

1.751

631

$18,917

5.074

632

$17,431

4.272

633

$17,044

3.868

634

$14,870

2.009

635

$19,384

2.256

701

$18,250

2.471

705

$14,212

3.019

706

$15,817

2.154

710

$21,911

5.190

711

$19,282

4.579

712

$21,795

3.717

713

$22,904

3.720

713

$22,507

6.127

714

$19,592

4.468

714

$16,900

2.110

718

$12,818

0.782

718

$9,849

0.259

719

$16,931

1.233

719

$23,545

3.288

720

$9,198

0.235

721

$22,190

1.406

721

$19,646

2.206

724

$24,750

5.650

726

$18,140

5.078

728

$21,250

1.433

731

$22,231

7.452

731

$19,788

5.738

735

$13,269

1.364

Data taken from U.S. Bureau of Census 1980 Pierce County, WA; Reprinted in Brown, W.S., Introducing Econometrics, St. Paul (1991): 198-200.

When we run our regression, we get the following equation:

Ŷ= 0.000297*Income – 2.221

Both the intercept and independent variable’s parameter estimates are significant, with the intercept parameter having a t-ratio of -4.094 and the income estimate having one of 9.182. R2 is 0.597, and the F-statistic is a strong 84.31. The model seems to be pretty good – strong t-ratios and F-statistic, a high coefficient of determination, and the sign on the parameter estimate for Income is positive, as we would expect. Generally, the higher the income, the greater the Own-to-rent ratio. So far so good.

The problem comes when we do a visual inspection of our data: first the independent variable against the dependent variable and the independent variable against the regression residuals. First, let’s take a look at the scatter plot of Income and OwnRatio:

Without even looking at the residuals, we can see that as median family income increases, the data points begin to spread out. Look at what happens to the distance between data points above and below the line when median family incomes reach $20,000: OwnRatios vary drastically.

Now let’s plot Income against the regression’s residuals:

This scatter plot shows essentially the same phenomenon as the previous graph, but from a different perspective. We can clearly see the error terms fanning out as Income increases. In fact, we can see the residuals diverging at increasing rates once Income starts moving from $10,000 to $15,000, and just compounding as incomes go higher. Roughly half the residuals fall on both the positive and the negative side, allowing us to meet the regression assumption of our residuals having a mean of zero, hence our parameter estimates are not biased. However, because we violated the constant variance assumption, the standard error of our regression is biased, so our parameter estimates are suspect.

Visual Inspection Only Gets You So Far

By visually inspecting our residuals, we can clearly see that our error terms are not homoscedastic. When you have a regression model, especially for cross-sectional data sets like this, you should visually inspect every independent variable against the dependent variable and against the error terms in order to get a priori indication of heteroscedasticity. However, visual inspection alone is not a guarantee that heteroscedasticity exists. There are three particularly simple methods to detecting heteroscedasticity which we will discuss in next week’s Forecast Friday post: the Park Test, the Goldfeld-Quandt Test, and the Breusch-Pagan Test.

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Doing Market Research for Your Business Plan Need not be Expensive

June 2, 2010

Every business needs to do market research. Whether your company is a Fortune 500 corporation or the neighborhood bar, understanding the market or markets in which you operate is critical to your company’s success. Would you invest money in an oil company that didn’t research the fields where it wanted to drill? Would you buy a house in a neighborhood without checking out the schools, crime rate, or housing market? Would you open a restaurant if you knew nothing about the location, the traffic around it, or the prospective customers? You can be sure that if you wanted to open a business, no banker will loan you money without you having done proper, thorough market research.

When one hears the phrase “market research,” most often he/she thinks about surveys and focus groups. These are the most common, yet often most expensive types of market research. Surveys and focus groups are primary research methods, since they are conducted from scratch. Most market research that small businesses need is secondary, that is, research that has already been conducted, published, and available to the public. Often, secondary research can be found in libraries, online, or through other published sources. Secondary research is also much less expensive – sometimes even free – to obtain; however, sifting through it for information relevant to your business’ needs and analyzing it properly can be very time-consuming. In this post, we will discuss how someone starting a business can do market research without breaking the budget.

First Step: Decide on the Information You Need

Tom Johnson has decided to fulfill his dream of starting a comedy club. He’s purchased a book on writing a business plan, and finds that one section of a typical business plan is “Market Analysis.” Tom realizes he must get this section down pat in order to determine the viability of his business and make projections of his first few years of revenues, and convince a banker to lend him money. Tom needs to ask himself several questions: What type of customers am I catering to? What locations are most convenient for attracting those customers? What are the traffic patterns in those locations? What other comedy clubs and entertainment venues are in the area? What do they charge? How do they promote their businesses? What types of promotions do my target customers respond to? Tom writes down all the questions he can think of that will help him analyze his market.

Census Bureau

The first place Tom turns to is the U.S. Bureau of the Census. The bureau’s Web site, www.census.gov, provides a wealth of info for him. He looks at the Web site for demographics, and plugs in the ZIP codes for the locations he is considering, along with their adjacent ZIP codes. The Web site provides great insights into the number of households in the ZIP code, the age ranges, income levels, racial composition, and other demographic factors. Also from the bureau’s Web site, Tom obtains the latest “Consumer Expenditure Survey,” and finds out what the average family spends on entertainment each year.

Tom then notices that the bureau also does an Economic Census of businesses every five years. He finds the Web page for County Business Patterns and looks to see how many entertainment establishments are within the ZIP codes he is considering. He gets good insights about the number of establishments, their employee size, revenues, and payrolls. Tom also finds other interesting facts from the Economic Census – particularly what percentage of revenues entertainment establishments typically spend on various categories: advertising, salaries, maintenance, etc.

Local Library

Tom realizes the Census Bureau has provided him with data that is summarized and aggregated. He needs more information about specific competitors and business patterns in the areas he is considering. So he visits his local library, which has access to several different databases of small businesses, like Dun & Bradstreet’s Hoover’s, and Million Dollar Database. These databases provide information on several individual establishments, including revenues, owner/officer information, employees, and location. Tom does a search of all entertainment establishments in his locations of interest.

Tom also searches through local newspapers of the past few weeks to see which entertainment venues were advertising, how often they were advertising, what they were offering in their ads, etc. He then goes to the Yellow Pages to see if those prospective competitors advertise there as well.

Chambers of Commerce

Tom then contacts different chambers of commerce around his locations of interest. He finds out when their functions are and attends some of them. The local chambers of commerce are great sources for identifying the similar businesses in his area, meeting their owners directly, and finding other businesses that can be help to Tom in opening his business. For example, Tom could meet the general manager of a local movie theater, and might learn from him that the area seems to be pressed for customers, or is impacted by some local ordinance; Tom might also meet a banker or an attorney who specializes in helping new businesses start. Still, he might meet people from a local corporation who are seeking to do events for employees, of which a comedy club can be a great option. Tom might also find information on the cost of labor in the area, as well as commercial real estate rents in various areas. Chambers of commerce are ideal for networking, news, assistance, prospective customers, and other information.

Getting Out There

Tom has now done a lot of secondary research, an exhaustive amount if you ask me! But there is also some primary research he can – and must – do. Tom should drive the areas near the proposed locations for his comedy club. He should check out the other entertainment places nearby: restaurants, jazz/dance clubs, movie theaters, other comedy clubs, karaoke bars, etc. That is, he should mystery shop. Tom should go into some of these competitors and get a feel for the type of clientele to which they cater, the prices they charge, the quality of service they deliver, and how busy they are. He can also see the décor of these venues, their peak times, the outdoor signage, and the traffic around them. All of these can yield valuable clues about the venue’s degree of competitive threat to Tom’s comedy club, and the viability of the location.

Putting it all Together

While there are countless many more sources Tom can turn to for market research, we see he’s done quite an impressive amount already. While most of his sources were free, or of minimal cost, Tom’s real expense was the time and legwork he put into it; he must now synthesize all this information and analyze it to see which locations provide the best mix of traffic, revenue potential, rental costs, and demographics, and then use that information to create forecasts. Once he’s done that, Tom can write the Market Analysis section.

PlanPro Makes the Market Analysis Section of Your Business Plan a Snap!

Chances are you don’t have the time Tom did to do all of that research. Finding all that secondary information and making heads or tails of it is probably something you’d rather delegate to a professional. With PlanPro, Analysights conducts all the secondary research you need for your business, and provides you with templates for the primary research you need to do. Once all the research is compiled, we will analyze it and provide you with the findings, so that you could write the Market Analysis section of your business plan with ease. All for a flat $495! For an extra $125, we will also write the Market Analysis section for you. This way, you can spend more time on the elements of your business plan that make the best use of your time. To learn more about PlanPro, visit: http://analysights.com/PlanPro.aspx or call Analysights at (847) 895-2565.

Small Businesses Can’t Afford to do Marketing Research? They Can’t Afford NOT To!

September 21, 2009

How many of us would go on a road trip without first determining the optimal route to our destination?  Or locating the lodging facilities, restaurants, and service stations along the way?  Yet, why is it that when it comes to running our business, many of us don’t take the time to research the route to our business’ success?

Marketing research is a key component in developing effective marketing and business plans.  Marketing research helps us understand who our customers are, what their needs and wants are, and how they perceive our companies and our products vis a vis our compeition; marketing research also helps us ascertain how viable the market is for our products and services, the degree of competition, and the trends within our industry; and marketing research helps us establish goals and choose courses of action.

Yet many small business avoid doing any marketing research because they perceive it to be very costly.  However marketing research exists in several forms, many low cost or even free.  There are two types of marketing research data: primary and secondary.  Primary research is information you collect directly from the customer through surveys or focus groups.  Secondary research is information that has been collected and published by various organizations such as government agencies, trade publications and associations, and chambers of commerce, for various purposes.   Secondary research tends to be the least costly of the two, so it will account for the vast majority of market research a small business conducts, and most often will be all it needs.

Doing Marketing Research on a Shoestring

How can a business do marketing research on a low budget?  There are lots of great secondary research sources available, often for the nominal cost of a trip to your local library or an Internet search.  One of the best sources of marketing research data is the U.S. Census.  The Census Bureau provides demographics and population estimates, as well as social, political, and economic data.  The Census Bureau also conducts an Economic Census every five years to measure industrial activity.  The Economic Census breaks statistics down by industry and region, enabling you to size up your competition.  You can find out how many firms are in your territory, how big they are, what their revenues are, etc.  You can even find out how much of the industry’s sales are controlled by the top companies.

Besides the Census Bureau, you can find inexpensive data from your chamber of commerce, your trade associations, your vendors, and even your customers.  Check out the Encyclopedia of Associations, by Gale Research, at your library.  This source can help you identify associations relevant to your industry, as well as associations your customers might be members of.

Your public library will also have sources like The Thomas Register of American Manufacturers and the Harris InfoSource All-Industries and Manufacturing Directories, which can help you target businesses in a certain industry, learn more about competitors, and find companies to manufacture your products.

If you’re looking for company-specific information, your library may have an online subscription to Hoover’s, which is owned by Dun and Bradstreet.  In fact, D&B also furnishes its Million Dollar Database, which provides addresses, key officers, sales, and number of employees for almost 2 million U.S. and Canadian organizations, both publicly traded and privately owned.

Secondary information can also be obtained from colleges and universities, community organizations, and other government agencies.

And this list is far from comprehensive.

Given all the secondary information at our fingertips, the question is no longer whether small businesses can afford to do marketing research, but whether they can afford not to.