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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 - b₁x̄

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