Chapter 3 Phrasing and Equations

Interpretation of Y - Hat

The average [output variable] for the given [input variable].

Interpretation of Slope

Average [increase or decrease] in [y] per unit increase in [x].

Interpretation of r²

[r²x100] % of the total variation in the [output] is explained by the linear model relating the [output variable] to the [input variable].

Interpretation of the Standard Deviaton of Residuals

The typical distance between the actual [output] value and the predicted [output] value with the given [explanatory variable] value.

Equation for Simple Linear Regression (Sample)

ŷ = b₀+b₁x

Equation for Simple Linear Regression (Population)

y= b₀+b₁x+ε

Equation for Residual

Residual = y(observed) - ŷ

Equation for the Total Sum of Squares

∑(y - ȳ)²

Equation (in words) for r²

Variation Explained by the Model / Total Variation in the Output Data

Equation for slope (b₁)

b₁ = r * (sy / sx)

Equation for y-intercept (b)

b = y̅ - b₁x̄