24 february 2012 9 18 formula of course there is a

This preview shows page 9 - 15 out of 18 pages.

24 February 2012 9 / 18
Image of page 9

Subscribe to view the full document.

Formula Of course, there is a formula for r , the sample correlation. r = 1 n - 1 n X i =1 x i - ¯ x s x y i - ¯ y s y We’ll work some example of this out later. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 10 / 18
Image of page 10
The Regression Model When doing regression, we’re going to assume that each observation ( y i ) is generated (e.g. created by Mother Nature) according to a model. This model will change and get progressively more complicated over the next month. For simple linear regression, our model will be: y i = α + βx i + e i Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 11 / 18
Image of page 11

Subscribe to view the full document.

The Simple Linear Regression Model y i = α + βx i + e i α represents the Y intercept β represents the slope of the line x i represents the value of the explanatory variable for datum i y i represents the value of the response variable for datum i e i represents the random error present for datum i (assumed to be normally distributed with a mean of 0 and a standard deviation of σ ) Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 12 / 18
Image of page 12
The Fitted Line We’re using Greek letters here because this represents the true, unknown model: y i = α + βx i + e i What we’re going to do is estimate the values of α and β from the data. ˆ y i = ˆ α + ˆ βx i The little hats mean these are estimates. Douglas Whitaker (Statistics Department) STA 3024: Regression 24 February 2012 13 / 18
Image of page 13

Subscribe to view the full document.

The Fitted Values ˆ y i = ˆ α + ˆ βx i Notice that we have an estimated value for y i . This estimated value, ˆ y i
Image of page 14
Image of page 15
You've reached the end of this preview.

{[ 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