# Chapter 3 Phrasing and Equations

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Interpretation of Y - Hat

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## Description and Tags

### 11 Terms

1

Interpretation of Y - Hat

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

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2

Interpretation of Slope

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

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3

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].

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4

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.

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5

Equation for Simple Linear Regression (Sample)

ŷ = b₀+b₁x

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6

Equation for Simple Linear Regression (Population)

y= b₀+b₁x+ε

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7

Equation for Residual

Residual = y(observed) - ŷ

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8

Equation for the Total Sum of Squares

∑(y - ȳ)²

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9

Equation (in words) for r²

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

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10

Equation for slope (b₁)

b₁ = r * (sy / sx)

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11

Equation for y-intercept (b)

b = y̅ - b₁

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