{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CH10 Notes - Multiple Linear Regression Model Y = 0 1 x1 2...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Multiple Linear Regression Model Y = ß 0 + ß 1 x 1 + ß 2 x 2 + … + ß k x k + ε deterministic component random component ***Note: Linear w.r.t. Parameters ß 0, ß 1 … ß k and not predictor variables. Assumptions: 1. The specified regression model has the correct form . Therefore for given values of x 1 , x 2 , … x k , E(Y) = ß 0 + ß 1 x 1 + … + ß k x k and E(ε) = 0 This implies that when the least squares estimates are determined, the least squares equation Ŷ = b 0 + b 1 x 1 + … + b k x k estimates the average value of Y, given a set of values for the predictor variables x; and, the model correctly represents the form of the association between the response variable and the predictor variables. 2. The error variance is constant . The σ 2 ε is constant over all values of the predictor variables. Thus, the range of deviations of the Y- values from the regression model is the same regardless of the values of x 1 , x 2 , …,x k . 3. Random errors, ε’s, are independent and normally distributed . Hence, the random errors associated with the Y-values are statistically independent of one another and normally distributed. The residual variance S 2 e is defined by: S 2 e = SSE / (n-k-1) where SSE = ∑ (Y i – Ŷ i ) 2 S 2 e remains an absolute measure of how well the least squares equation fits the sample Y – values. If the fit were perfect, all residuals would equal 0 and S 2 e = 0.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Partitioning the Total Variation SST = SSR + SSE where _ _ SST = ∑(Y i –Y) 2 SSR = ∑(Ŷ – Y) 2 SSE = ∑( - Ŷ) Ү 2 The coefficient of determination has the same interpretation as in simple linear regression, that is, the fraction of the total variation in the sample Y-values that has been explained by the predictor variables in the least squares equation.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern