{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CH-15 PPT - Multiple Regression Analysis Introduction We...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Multiple Regression Analysis November 30, 2010
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
Introduction We can use the same ideas from simple linear regression to analyze relationships between a dependent variable and several independent variables Multiple regression is an extension of the simple linear regression for investigating how a response y is affected by several independent variables x 1 , ..., x k Our objectives are: - find relationships between y and x 1 , ..., x k - predict y using x 1 , ..., x k
Image of page 2
Examples Monthly sales ( y ) of a retail store may depend on x 1 = advertising expenditure x 2 = time of year x 3 = size of inventory x 4 = state of economy Body fat ( y ) may depend on x 1 = age x 2 = sex x 3 = body type
Image of page 3

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

View Full Document Right Arrow Icon
Pertinent Questions Which of the independent variables are useful and which are not? How could we create a prediction equation which allows us to predict y using knowledge of x 1 , x 2 , x 3 etc? How strong is the relationship between y and the independent variables? How good is the prediction?
Image of page 4
The General Linear Model y = β 0 + β 1 x 1 + β 2 x 2 + ... + β k x k + y is the dependent variable (response) x 1 , ..., x k are independent variables (predictors) The deterministic part of the model, E ( y ) = β 0 + β 1 x 1 + β 2 x 2 + ... + β k x k , describes average value of y for any fixed values of x 1 , ..., x k . The observation y deviates from the deterministic model by an amount is random error. We assume random errors are independent normal random variables with mean zero and a constant variance σ 2
Image of page 5

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

View Full Document Right Arrow Icon
The Method of Least Squares Data: n observations of the response y and the independent variables x 1 , ..., x k The best fitting prediction equation is ˆ y = b 0 + b 1 x 1 + b 2 x 2 + ... + b k x k We choose our estimates b 0 , ..., b k to minimize SSE = X ( y - β 0 - β 1 x 1 - β 2 x 2 - ... - β k x k ) 2 The computation is usually done by a computer
Image of page 6
Example A data set contains the college GPA ( y ), high school GPA ( x 1 ) and study time ( x 2 ) of 59 randomly selected students. We are interested in regressing college GPA on high school GPA and study time.
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
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