Author: Nathan Robinson

What are the assumptions of ordinary least squares (OLS) in econometrics
Financial Mathematics Topics

What are the assumptions of ordinary least squares (OLS) in econometrics

- by Nathan Robinson

Ordinary Least Squares (OLS) is the simplest and most widely used estimation technique in econometrics. It provides the Best Linear Unbiased Estimators (BLUE) for the parameters in a linear regression model, provided a specific set of assumptions, known as the Classical Linear Model (CLM) assumptions, are met.

When these assumptions hold, the OLS estimates are considered reliable and trustworthy for statistical inference. When they are violated, the results can be misleading, biased, or inefficient.

Here are the nine core assumptions of OLS, grouped by their impact on your model.

Group 1: Assumptions for Linearity and Data Quality

These assumptions ensure the model is correctly specified and the data is appropriate.

1. Linearity in Parameters

The relationship between the dependent variable and the independent variables must be linear in the parameters.

  • Formal Statement:
  • Implication: This does not mean the variables themselves must be linear; you can use transformations like
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How to Calculate Marketing Campaign ROI for Small Business
Calculating ROI for Business

How to calculate marketing campaign ROI for small business?

- by Nathan Robinson

For a small business, every dollar spent on marketing needs to work hard. Knowing whether your campaigns are generating profit or just burning cash is crucial for survival and growth. That’s where Marketing Campaign ROI (Return on Investment) comes in.

Calculating ROI isn’t just about simple arithmetic; it’s about connecting your marketing efforts directly to your bottom line. Here’s a step-by-step guide for small businesses on how to measure and interpret their marketing ROI.

Step 1: Define Your Total Campaign Costs

The first step is to accurately capture all expenses related to the marketing campaign. This goes beyond the direct ad spend.

Cost CategoryExamples
Direct SpendAdvertising budget (Google Ads, Facebook, print, radio), software subscriptions used for the campaign (e.g., email service provider).
Creative CostsFees paid to a graphic designer, photographer, copywriter, or video editor.
Time/Labor CostsThe hourly wage and time spent by your team (or yourself)
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Time Series Econometrics for Forecasting Stock Prices
Calculating ROI for Business

Time Series Econometrics for Forecasting Stock Prices

- by Nathan Robinson

Forecasting stock prices is one of the most challenging and sought-after goals in financial economics. While no model can perfectly predict the future (largely due to market efficiency and random walk theory), time series econometrics provides the rigorous framework necessary to model stock price dynamics, test for significant relationships, and generate informed forecasts.

Here is an overview of the key concepts and models used in applying time series analysis to stock price data.

Why Standard Regression Fails in Finance

The primary issue when analyzing financial data, such as daily or monthly stock prices, is the inherent violation of the core assumptions of Ordinary Least Squares (OLS) regression.

  1. Non-Stationarity: Stock prices often exhibit a trend over time, meaning their mean and variance are not constant. Non-stationary data leads to spurious regressions, where a high suggests a relationship that is statistically meaningless.
  2. Autocorrelation: The current price of a stock is highly
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Voice Search for Local Restaurants & Cafes
Education

Voice Search for Local Restaurants & Cafes

- by Nathan Robinson

In the fast-paced digital age, convenience is king. As technology becomes more integrated into daily life, voice search is rapidly changing how consumers find information—and that includes discovering their next meal. From asking smart speakers for the “best pizza near me” to using voice assistants on smartphones to find nearby cafes, customers increasingly rely on voice search to make dining decisions. These trends are now a vital focus of modern Digital Marketing Courses in Pune, where aspiring marketers are taught to adapt strategies to voice-enabled, mobile-first behavior.

Voice search is no longer a novelty; it’s a necessity. For local restaurants and cafes, optimizing for voice search can mean the difference between being found first—or not at all. Whether it’s a family looking for a weekend brunch spot or a traveler craving coffee, people are using voice commands for instant, location-based answers. So, how can local eateries adapt and benefit …

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Steps to Start a Commercial Property Management Company
Property Business

Steps to Start a Commercial Property Management Company

- by Nathan Robinson

Starting a commercial property management company is a complex but rewarding business venture. Unlike residential management, commercial properties—such as office buildings, retail centers, and industrial warehouses—involve high-value assets, specialized leases, and business-to-business (B2B) client relationships.

To build a profitable and reputable firm, you must follow a disciplined path focusing on legal compliance, specialized knowledge, and strategic scaling.

Step 1: Master the Commercial Real Estate Niche

Before you print business cards, you must define what you manage and prove you can do it well.

  • Choose Your Focus: Commercial real estate (CRE) is broad. Will you specialize in Retail (requiring knowledge of co-tenancy clauses and percentage rent), Office (focused on tenant improvements and building systems), or Industrial/Warehouse (concerned with logistics and specialized utilities)? Specialization allows you to charge premium rates.
  • Obtain Necessary Licensing: Most states require a valid Real Estate Broker’s License to perform property management services for others, as the duties
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