Notes7 SLR Spring 09

Notes7 SLR Spring 09 - Notes 7.1 of 22 Notes7: Simple...

This preview shows pages 1–5. Sign up to view the full content.

20 15 10 5 0 70 60 50 40 30 20 10 0 X Y Scatterplot of Y vs X 20 15 10 5 0 900 800 700 600 500 400 300 200 100 0 X Y_ Scatterplot of Y_ vs X Notes 7. 1 of 22 Notes7: Simple Linear Regression Text Sections 14.1 – 14.7 Regression analysis is a tool used to determine whether an independent variable Y is related to a dependent variable X . We assume that if there is a relation between these variables it takes the form of a linear relation. If there is a relation, we can use it for example to predict future values of Y if we know the value of X . Linear relation example: Y = 2 + 3 X Curvilinear relation example: Y = 2 - 20 X + 3 X 2

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

View Full Document
20 15 10 5 0 70 60 50 40 30 20 10 0 X Y Scatterplot of Y vs X 20 15 10 5 0 60 50 40 30 20 10 0 X Notes 7. 2 of 22 The linear relation Y = 2 + 3 X is an example of an exact or deterministic relation. If Y and X are related in this way, observed data points would fall on a line: In the real world, data points are more likely to randomly scatter around a line. This is a probabilistic relation . A mathematical ‘model’ or statement of this relation can be expressed as: Y = 2 + 3 X + ε where (‘epsilon’) represents a random error component of the model.
Notes 7. 3 of 22 In general, the simple linear regression model is expressed as: y = β 0 + β 1 x + ε where: β 0 and β 1 are the y -intercept and slope, respectively (these are unknown parameters in the model) y = the dependent or response variable x = the independent or predictor variable = the random error component Example: Suppose that the Steamboat Springs Chamber of Commerce is interested in the relation, if any exists, between a visitor’s income ( x , measured in \$1k units) and the amount that he or she spends per day on a vacation at Steamboat Springs ( y , measured in \$). (Why is y the natural choice for the dependent variable?) Data is obtained for ten randomly selected visitors. Case # x y x 2 xy y 2 1 14 54 196 756 2916 2 27 104 729 2808 10816 3 38 168 1444 6384 28224 4 19 82 361 1558 6724 5 43 188 1849 8084 35344 6 26 101 676 2626 10201 7 59 207 3481 12213 42849 8 37 141 1369 5217 19881 9 29 106 841 3074 11236 10 45 172 2025 7740 29584 Sums 337 1323 12971 50460 197775

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

View Full Document
60 50 40 30 20 10 225 200 175 150 125
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/26/2011 for the course STAT 201 taught by Professor Drex during the Spring '04 term at Drexel.

Page1 / 22

Notes7 SLR Spring 09 - Notes 7.1 of 22 Notes7: Simple...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online