April 3, 2013
Final Class: Continuing from last week
Regression analysis is a bunch of summary statistics telling us the relationship between an IV
and DV. They are summary because they tell us lots of direction: they tell us the direction, how
closely the variables are linked. The B value is a powerful determinant.
Analysis of the support for immigration. Look at the table. We can fill in the numbers of the
values into the formula and we will get an idea of the direction the line is going in.
Multiple Regressions: Other Features
• How substantial a role do IVs have?
• Two methods of evaluation: for evaluating the strength of the relationship of the
• 1. R-Squared
• 2. Beta
• Precise estimate of effect of an IV or set of IVs on DV captured by under standardized B
• Yet doesn’t explain how much of the variation in the DV is explained by the IV
• Recall our previous example looking at deferral news interest and international news
• Sao how good a job does the IVs do at explaining the DV? How well does the line of
best fit capture the pattern? This is where we get into how good is our model?
• This is the role of R-square
• How much better can we understand interest in international news by knowing interest in
• The mean score is our best guess to understanding the response of a bunch of people
that we know nothing about.
• Question of strength
• How much better than our best guess does our IV ass? Best guess….mean!
• Compares error from DV mean with error from regression line.
• Range is 0-1: If IV provides not contribution to understanding DV, closer to O, if IV
completely explains DV approaching 1. We can an R square of 1, the prediction id
perfect. The closer we are to 1 the closer we are to perfect.
• The red line should be capturing more responses than our best guess of the average,
which is represented with the green line in the graph.
• Can be interpreted as the proportion of the variation in the DV explained by the IVs. WE
want to explain the variations in responses to international news. The more we can
explain, (though R square), the greater portion we can explain why answers vary.
• Or the percentage improvement (if multiply by 100) in understanding the responses to
our DV, knowing our IV
• What’s good? No real answer, think about it as a jog saw puzzle with different sized
pieces, some are smaller and some bigger, but all important to understanding the
picture. • Our example? Federal politics and international news
• The adjusted r square is simply a small correction, almost entirely used when you have a
multi-variety model. It’s a conservative adjustment.
• We’ve been introduced to under standardized B values
• Under standardized B values are measured in the variable categories
• Ex. Education and interest in international news vs. interest in local news and interest in
international news: apples and oranges. They are not common themes.
• Betas are a way of standardized B values.
• The beta tells us how good our individual variables are, how much are they better than
the other variables.
• Remove specific variable categories, look at each relationship
• Based on changes in standard deviations
• Allow us to compare the influence of IVs in a multiple regression