sat104_lect7v1_1up

# sat104_lect7v1_1up - Stat 104 Quantitative Methods for...

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Stat 104: Quantitative Methods for Economists Class 7: Regression, a first look 1

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Correlation vs. Regression s A scatter plot can be used to show the relationship between two variables s Correlation analysis is used to measure the strength of the association (linear relationship) between two variables b Correlation is only concerned with strength of the relationship b No causal effect is implied with correlation b In correlation, the two variables are treated as equals. In regression, one variable is considered independent (=predictor) variable ( X ) and the other the dependent (=outcome) variable Y . 2
Regression Analysis s Regression analysis is a statistical technique that attempts to explain movements in one variable, the dependent variable , as a function of movements in a set of other variables, called independent (or explanatory ) variables through the quantification of a 3 single equation. s However, a regression result no matter how statistically significant, cannot prove causality . All regression analysis can do is test whether a significant quantitative relationship exists. s Model Assumption: Y and the X’s are linearly related.

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Some Notes and Terms s In Simple Linear Regression, one X variable is used to explain the variable Y s In Multiple Regression, more than one X variable is used to explain the variable Y. s For now we will concentrate on simple regression. 4
Example s Suppose we want to predict the sale price of used Honda Accords. s Many factors influence the price of a used car; odel year, condition, transmission type, 2 or 4 model year, condition, transmission type, 2 or 4 door, color, mileage, how badly owner wants to sell, etc. ... s We will choose just the variable mileage and see if price can be predicted from the mileage of the car. 5

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s X = mileage of the car s Y = price of the car s We suspect that the price of the Accord depends on its mileage to some extent. So if you just knew an Accord’s mileage but not it’s price maybe you could guess (or predict) it’s price. s To see if this would work, let’s collect some data where you know both price and size and see if there is a relationship. 6
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## This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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sat104_lect7v1_1up - Stat 104 Quantitative Methods for...

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