y = β₀ + β₁x + ε

In the context of this equation:

y stands for the dependent variable (the outcome)

x acts as the independent variable (the predictor)

β₀ is the intercept (value of y when x equals 0)

β₁ indicates the slope (change in y per one-unit increment in x)

ε represents the error term (difference between the observed and the forecasted values)

y = β₀ + β₁x₁ + β₂x₂ +... + βₚxₚ + ε

Here:

x₁, x₂,..., xₚ denote the independent variables

β₁, β₂,..., βₚ are the coefficients that mark the effect of each independent variable on the dependent variable

Linearity: There is a linear relationship between dependent and independent variables.

Independence: Observations exist independently of one another.

Homoscedasticity: The variance of the error term stays constant across independent variable values.

Normality: The error term subscribes to a normal distribution.

However, despite their widespread use, linear models also have their shortcomings:

Linearity assumption: The assumption of linearity inherent in these models may not always be valid in real-world scenarios.

Multicollinearity: The presence of highly correlated independent variables can give rise to unstable coefficient estimates, thus undermining the model's predictive capacity.

The U.S. corn exports data showcases the annual quantity of corn that the United States trades with foreign countries.

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