Download presentation

Presentation is loading. Please wait.

Published byAlfred Grayer Modified over 3 years ago

1
Multivariate Data/Statistical Analysis SC504/HS927 Spring Term 2008 Week 18: Relationships between variables: simple ordinary least squares (OLS) regression

2
2 Outline What is regression analysis? Scatter plots Linear regression Terminology and notation Interpreting a regression equation Putting it into practice

3
3 What is regression analysis? A statistical technique for: analysing the association between variables (e.g. how is alcohol consumption related to income on average ?) making conditional predictions (e.g. what do we expect to happen to smoking behaviour if tobacco taxes increase?) testing hypotheses about the nature of conditional relationships (e.g. on average do crime rates vary in proportion to unemployment rates?) summarizing/describing data on 2+ variables

4
4 Scatterplot of suicide against unemployment rates

5
5 How do we summarise the relationship between suicide and unemployment rates? Assume a straight-line (linear) relationship between suicide rate (y) and unemployment rate (x): y=a + bx Estimate a and b by applying ordinary least squares regression to the data in the scatter plot: estimate of a = 1.435 estimate of b = 0.324

6
6 Method of Least Squares A method of finding the line that best fits the data The line of ‘best fit’ is found by ascertaining which line, of all possible lines, results in the least amount of difference between observed data points and the line

7
7 Scatter with fitted line

8
8 Interpretation y=1.435 + 0.324x if unemployment (x) is zero, suicide rates are predicted to be 1.435 per 100,000 population each 1 percentage point increase in unemployment increases the predicted suicide rate by 0.324 relationship between y and x is not exact so we usually write: y=a + bx + e

9
9 Terminology and notation y i =a + bx i + e x i and y i are variables which have different values for each individual/ observation they vary across cases in dataset (i refers to case (individual) i) y=dependent variable x=independent variable a and b are unknown (not observed) constants a and b are population parameters a and b are to be estimated from sample data e is error/disturbance/residual term

10
10 a is the y-axis intercept a 0 x y

11
11 b is the slope or coefficient of x a 0 x y b 1

12
12 A note on causality Just because we write: y i =a + bx i + e Does not mean x causes y Suppose y = income, x = whether or not someone is an owner-occupier would turning renters into homeowners increase their incomes? or is it that you need a good income to be able to purchase a home? or that people on low incomes are more likely to be eligible for social rented housing

13
13 What is the relationship between suicide and unemployment? Which is your ‘dependent’ variable? Use Graphs – scatter- simple- define-OK Double click on chart. Go to: Elements-Fit line at Total. You can also change axes by going to: Edit- Select Y [X] axis For the values, use Analyse – regression - linear

14
14 SPSS Output R =.702 (simple correlation between suicide and unemployment) R² =.493 (unemployment rates can account for 49% of the variation in suicide rates)

15
15 a = intercept (constant) = 1.435 b = gradient (unemployment rate per 100) =.324 In 1997, the unemployment rate was 1 (per 100) therefore…… Suicide rate = 1.435 +.324 x 1 = 1.759 (per 100000)

Similar presentations

OK

C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Linear Regression and Linear Prediction Predicting the score on one variable.

C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Linear Regression and Linear Prediction Predicting the score on one variable.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on high voltage engineering corp Ppt on online shopping cart project Ppt on solar system for class 6 download Ppt on different types of forests Ppt on object oriented programming with c++ textbook Ppt on forest conservation act Download ppt on data handling for class 7 Ppt on tcp ip protocol tutorial Free ppt on sources of energy Ppt on series and parallel circuits worksheets