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Mahasiswa dapat melakukan fitting model Menggunakan Regresi Linier Berganda beserta komputasi-nya

Tujuan perkuliahan

MULTIPLE LINEAR REGRESSION

Another useful extension of linear regression is the case where y is a linear function of two or more independent variables. For example, y might be a linear function of x1 and x2, as in

y = a0 + a1x1 + a2x2 + e

Such an equation is particularly useful when fitting experimental data where the variable being studied is often a function of two other variables. For this two-dimensional case, the regression “line” becomes a “plane”

MULTIPLE LINEAR REGRESSION

As with the previous cases, the “best” values of the coefficients are determined by formulating the sum of the squares of the residuals:

MULTIPLE LINEAR REGRESSION

and differentiating with respect to each of the unknown coefficients:

MULTIPLE LINEAR REGRESSION

and differentiating with respect to each of the unknown coefficients:

MULTIPLE LINEAR REGRESSION

The coefficients yielding the minimum sum of the squares of the residuals are obtained by setting the partial derivatives equal to zero and expressing the result in matrix form as

MULTIPLE LINEAR REGRESSION

MULTIPLE LINEAR REGRESSION

MULTIPLE LINEAR REGRESSION

MULTIPLE LINEAR REGRESSION

MULTIPLE LINEAR REGRESSION

where the standard error is formulated as

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and the coefficient of determination is computed with Eq. (14.20).

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Although there may be certain cases where a variable is linearly related to two or more other variables, multiple linear regression has additional utility in the derivation of power equations of the general form

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Such equations are extremely useful when fitting experimental data. To use multiple linear regression, the equation is transformed by taking its logarithm to yield

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