ST211 Lecture 2.pdf

ST211 Lecture 2.pdf - ST211 Applied Regression Simple...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
ST211 Applied Regression
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
We could say a lot about what is meant by a model, and the modelling process. We condense the discussion by saying that many natural world phenomena can be represented by a mathematical equation, the model: • E = mc 2 (Relativity Law) • v 2 = u 2 +2as (Newton’s Laws of Motion) • Production = K* Labour α (Cobb-Douglas Relation) • H = Acoswt + Bsinwt (Height of tide in a harbour) • D = α + βA + γA 2 (Drying time of paint as a function of amount of additive used) • V = β 0 1 F + β 2 B + β 3 G + β 4 A + … (Value of a property in terms of floorspace F, number of bathrooms B, garden size G, age A and more) etc. Simple Linear Regression (SLR)
Image of page 2
Simple Linear Regression (SLR) In its basic form, simple linear regression involves finding – and then analysing – a model that takes the form y = α + βx. We later include an error term to account for Imprecision of the estimates we find. Such models are simple because there is only a single predictor x, in contrast with multiple regression with several predictors; and linear because y is a linear function of x and not x 3 , log x or whatever. We shall look briefly at some important features of SLR. However, the main part of the description will be in the context of multiple regression, which is really an extension of SLR, as we shall see.
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
Simple Linear Regression When we want to carry out SLR, we should routinely produce a scatterplot. This will provide a quick check on linearity as well as drawing out any unusual features of the data, such as outliers. Linear models do occur in practice: fuel consumption of aircraft with distance travelled weight by height of a group of animals value of a property from area of floor space sales of scarves by temperature etc. But as we shall see later, an improved model may generally be achieved by including other variables, such as garden size and age of a property as well as floor space.
Image of page 4
Simple Linear Regression We assume that we are given pairs of data (x 1 , y 1 ), (x 2 , y 2 ), … (x n , y n ). We seek the ‘line of best fit’ for these data, that is, the line y = α + βx for which the distance from points to line is as small as possible. A natural criterion is to use Here LSE, stands for Least Squares Estimate, y obs is an observed value of y, while y mod is the corresponding modelled value.
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
Image of page 6
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