University:
California State University, Northridge
Course:
MATH 540 | Regression Analysis
Academic year:

2003
Views:

375

Pages:

25
Author:

bobine4zr

Title: Regression Analysis Given: X, an ordinary variable which can be measured without appreciable error Y, a random variable, where Y is hypothesized to have some dependence on X Method of Least Squares: Developed by Gauss "Fits" hypothesized curve to the (X, Y) pairs of data Minimizes the sum of the squared distances, measured in the Y direction, from the points to the curve. Consider a simple case in which the curve is a straight line: y = β₀ + β₁x Diagram: A scatter plot showing a straight line (y = β₀ + β₁x) and a data point (xi, yi). The vertical distance between the data point and the line is labeled as Ei. The distance from the point (xi, yi), on the line y = β₀ + β₁x, to the point (xi, yi), where x = xi, may be written as: Ei = yi - y = yi - (β₀ + β₁xi) The error, Ei, is called the residual. Title: Parameter Estimation Confidence Intervals 2-sided For the Intercept, β₀: Determine n, x̄, β₀, Sxx, and σ² (as previously defined) Select α = significance level Then c = critical value t-distribution value corresponding to α/2 with (n-2) degrees of freedom Determine k = c * √(σ²/n + σ² * x̄²/Sxx) Then CONF(1-α){(β₀ - k) ≤ β₀ ≤ (β₀ + k)} Title: Parameter Estimation Confidence Intervals For the Regression Line (i.e. Mean): μŷ = β₀ + β₁x₀ Determine: n, x̄, Sxx, and σ² (as previously defined) ŷ = β₀ + β₁x₀ → for a particular x₀ Select α = significance level Then c = t-distribution value Corresponding to α/2 with (n-2) degrees of freedom Determine: k(x₀) = c * √(σ²/n + (x₀ - x̄)²/Sxx) standard error of the mean on the regression line → for the particular x₀ Then: CONF(1-α) { [ŷ(x₀) - k(x₀)] ≤ μŷ ≤ [ŷ(x₀) + k(x₀)] }

Regression Correlation

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