Week 7 notes
Week 7 notes Comm106
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This 2 page Class Notes was uploaded by Erica Evans on Monday February 22, 2016. The Class Notes belongs to Comm106 at Stanford University taught by Jennifer Pan in Fall 2016. Since its upload, it has received 8 views. For similar materials see Communication Research Methods in Communication Studies at Stanford University.
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Date Created: 02/22/16
Comm106 2/19/2016 Statistics • If we change one unit of one thing, how will that change the other thing? • Linear regression! à we assume there is a linear relationship • Y = a + bx à High school algebra equation for a straight line • For any value of x, we get some expected value of y • Suppose we have two points and draw a straight line between them, we can represent this as an equation. The slope is the rise/run. Y = y-‐intercept + slope*x. Writing equations • Population relationships are written in Greek letters • Our estimates from the sample are written with ‘hats’ • Y is the actual value of y in the sample y(with a hat) is what we predict based on the regression line Regression • Lets us predict y for any value of x • On average y changes by (b)(y’s units) for a 1 (x’s units) increase in x • If we are looking at the relationship between basketball player’s height and number of blocks in a game à On average a player’s blocks per game changes by .108 blocks for a 1 inch increase in height. • To predict y for any x, just plug in the numbers • Residual: the difference between the actual value and the predicted value • OLS estimation (ordinary least squares estimation) à the technique used to draw the line of regression • Drawing a line through the points to minimize the residuals. There are different ways to draw lines of regression; this is a specific method. • à Minimize the total squared vertical distances from the actual data points in the sample. Minimize the sum of the squared residuals. • Another technique is least absolute distance… this will also produce a straight line! • In regression, units matter! (Unlike correlation) à like switching from Celsius to Fahrenheit will change your equation. • Linear regression is asymmetric while correlation is symmetric à Y on X is not the same as X on Y. Comm106 2/17/2016 How to analyze a graph: • Pattern: What is the shape? Curvilinear? Linear? No pattern? • Direction: negative or positive? • Strength: how close are the points to each other? Does it look consistent? • Are there exceptions? • Correlation coefficient: how closely does the data follow a straight-‐line trend and how closely does the data cluster to that line? • R can be any value from -‐1 to 1 • 1 means perfect positive linear correlation • -‐1 means perfect negative linear association • 0 implies no association • Correlation formula: • X = 1,2,4,1 (average =2, sd =1.41) • Y = 1,3,4,3 (average =3, sd=1.63) • Z-‐score = number-‐average/sd • Multiply the corresponding z scores to get 4 numbers then add them all togetherà divide by n-‐1 (which is 4-‐1 in this case) • R = (.87+0+1.74+0)/3 = .87 • Function in R à cor() • Correlation is symmetric – x and y, is same as y and x. That’s why it doesn’t matter what order your input the variables in R Be careful • Sometimes observations are stacked on the same point in a scatter-‐plot
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