What is the estimated regression equation I am confused with

What is the estimated regression equation? I am confused with the response and predictor,

Consider the addition of the independent variable Food/Dining, i.e., develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursion and Food/Dining.

Solution

The response variable is the dependent variable and predictors are the independent variable. They work in the regression model as their name says. Let us assume that the regression model is-

y = b₀ + b₁ x₁ + b₂ x₂

So, the word predictor means anything that predicts outcome. So in this equation \'y\' can\'t give us anything until and unless we give it some value of x₁ and x₂. So, \'y\' is dependent on x₁ and x₂ . But the values of x₁ and x₂ are independent of anything. So, they are called the pedictors.

And once we have decided the values of predictors, then the outcome is predicted by the variable \'y\'. So, we call it a predictor.

Estimated regression equation is nothing but the mathematical representation of the relation between the dependent and the independent variable. The coefficients b₀ and b₁ are the least square estimates (generally). So we call it an estimated regression equation.

If we initially had only one independent variable (say Excrusion), then the regression equation for the Overall score would be -

Overall Score = Intercept + Slope (Excursion)

That means - y = b₀ + b₁x.

Now if another variable (say Food/Dining) is added then the regression equation will now have 2 independent variables written as -

y = b₀ + b₁x₁ + b₂x₂.

Where, x₁is the variable Excursion and x₂ is the variable Food/Dining.