data analysis: relationships continued regression research methods dr. gail johnson
Post on 14-Dec-2015
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Simple Regression
• Enables us to estimate the:• Strength of relationship
Expressed as the percent of variance explained
• How much change you can expect in the dependent variable based on a one unit change in the independent variable
• Enables you to make predictive estimates
Relationships
Correlation is not causation.
Statistical measurement includes the measurement of relationships. There are 2 ways to measure the strength of a relationship:
1. How great a difference the independent variable makes on the dependent variable (sometimes called the effect-description). This allows you to predict the effect of the IV on the DV but you have to have interval data.
Relationships
2. How completely the dependent variable is explained by the independent variable. (Correlational). (R squared).
Simple Regression
• Assumes a linear relationship
• Interval level (or dichotomous: which means coded 0 or 1) data
• Independent Variable: interval level
• Random or census
Simple Regression
Y = a + bX + error
Where:a = the constant or Y interceptb = the regression coefficient, or slopeY = predicted value of the dependant
variableX = the independent variable.
Simple Regression
• Estimate car repair costs for motor poolY= car repair costsX = miles driven
• Collect data and crunch it. You get these results:
Y = -267 and .018X
Simple Regression
• Estimate car repair costs
Y = -267 and .018X
• Interpretation: for every mile driven, the repair costs
goes up by 1.8 cents.For every 100 miles driven, costs go
up by $1.80
Simple Regression
• Y = -267 and .018X
• If you expect the cars to be driven a total of 100,000 miles, how much will car repair costs likely be?100,000 x .018 = $1,800
• Solve equation:Y = -267 + 1,800 = $1,763
Simple Regression
r= correlation coefficient (overall fit) (measure of association but non-directional; zero-order correlational coefficient).
r2 = proportion of explained variation
1-r2 = proportion of unexplained variation
Life is more complex
• Rarely will any one single variable cause something to happen
• Life is inherently multivariate
• What are the possible causes for urban decay?
What are the possible causes for urban decay?
• lack of jobs• high % of absentee
landlords• low % of homeowners• poor quality of
schools• increased
concentration of poor
• increase in drugs, crime
• aging housing stock• flight of middle class
to suburbs• corruption• aging infrastructure• business flight to
suburbs
What caused drop in crime?
• Changing demographics?
• Better policing?• Strong economy?• Gun control laws?• Concealed weapons
laws?• Increased use of death
penalty?
• Increase in number of police?
• Rising prison population?
• Waning Crack epidemic?
• Legalization of abortion?
Multiple Regression
• Multiple Regression lets you do four things: test your hypothesispredict the dependent variable if you know the
values for independent variablesPredicts the independent effect of each independent
variable while controlling for the others tells you the relative strength of each of the
independent variable using the beta weights
Multiple Regression
Y = a1 + bX1 + bX2 + bX3 + b X4 + e.Y = dependent variableX1 = independent variable 1,
controlling for X2, X3, X4X2 = independent variable 2
controlling for X1, X3, X4X3 = independent variable 3
controlling for X1, X2, X4X4= independent variable 4
controlling for X1, X2, X3
Multiple Regression
Income as a function of education and seniority?
Y = Income (dep. Var.)Y (Income) = a + education + seniority
Y= 6000 + 400X1 + 200X2based on Lewis-Beck example
Multiple Regression
Y= 6000 + 400X1 + 200X2
R square. = .67
67% of the variation in income is explained by these two variables. Excellent!
For every year of education, holding seniority constant, income increases by $400.
For every year of seniority, holding education constant, income increases by $200.
Multiple Regression
Y= 6000 + 400X1 + 200X2
Example:
Estimate the income of someone who has 10 years of education and
5 years of seniority:
Y=6000 + 400(10) + 200(5)
Y= $ 11,000
Multiple Regression
Relationship between contributions to political campaigns as a function of age and income?
Y= campaign contribution (dollars)
x1 = age (years)
X2 = income (dollars)
Multiple Regression
Relationship between contributions to political campaigns as a function of age and income.
Y = 8 + 2X1 + .010X2
(age) (income)
For every increase in age, contributions go up by $2.
For every increase in income, contributions go up .01 dollars
Multiple Regression
Y = 8 + 2X1 + .010X2
Y= campaign contribution (dollars)
But which is stronger?
Need to look at the Beta weights
Age = .15
Income = .45
Quick Analysis
• Whenever you are dealing with a correlation (regression analysis)
• First check the R squared value.• A good study will have this• If it is low, then you know that it is not a
strong model and they shouldn’t be making grand conclusions
• Make sure they meet 4 conditions necessary for causality
Example
• Study tried to determine what explained why some cities introduced reinvention.
• Sent out a survey, respectable response rate• Tested 13 factors they thought would
explain reinvention• R squared was .05• What do you conclude?
Example
• They ran a second model
• Included managers’ attitudes about innovation
• R squared was .22
• What do you conclude?
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