Final answer:
In an OLS model, assumptions include a linear relationship, normally distributed and homoscedastic errors, independence of residuals, and well-designed randomness in data collection. These assumptions are critical for valid model estimates and for minimizing chance error and bias.
Step-by-step explanation:
The underlying assumptions made about the error of an OLS model (Ordinary Least Squares) play a crucial role in the validity of the model's estimates. One fundamental assumption is that there is a linear relationship between the independent and dependent variables. Another assumption is that the residuals, or errors, are normally distributed and that they have the same variance (homoscedasticity), indicating that the spread of y values around the line of best fit is consistent, regardless of the value of x.
Additionally, it is assumed that the residuals are independent from one another, meaning there should be no discernible pattern in the way errors are distributed, often referred to as no autocorrelation. Moreover, if one is concerned about Type II errors, various factors such as sample size, effect size, and total variance need to be carefully considered to ensure the power of the statistical test.
The presence of chance error and bias are two types of errors that could occur, which may distort the results of the study. For accurate OLS model estimations, the data should stem from a well-designed random sample or randomized experiment.