Linear Regression

Perform Ordinary Least Squares (OLS) regression for simple or multiple predictors.

#
n = 0Outcome
n = 0Risk Factor
1
2
3
4
5
6
7
8
9
10
10 Rows Γ— 2 Columns

Linear Regression

Enter data to run the Ordinary Least Squares (OLS) regression.

Formula

Linear Regression (OLS)

Model Equation:

Y=Ξ²0+Ξ²1X1+...+Ξ²kXk+Ο΅Y = \beta_0 + \beta_1 X_1 + ... + \beta_k X_k + \epsilon

Coefficients Estimate Matrix Form:

Ξ²^=(XTX)βˆ’1XTY\hat{\beta} = (X^T X)^{-1} X^T Y

F-Statistic:

F=MSRMSE=SSR/kSSE/(nβˆ’kβˆ’1)F = \frac{MSR}{MSE} = \frac{SSR / k}{SSE / (n - k - 1)}

Where:

  • XX = Design matrix
  • YY = Response vector
  • SSR = Regression Sum of Squares
  • SSE = Error Sum of Squares