(Exam 2) SimpleRegression 11

# (Exam 2) SimpleRegression 11 - Simple Linear Regression...

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Simple Linear Regression Prediction Using One Predictor

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Prediction
Pearson

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Scatterplot: TWO variables Relationship between TWO continuous variables Grades and Studying Age and Memory Height and Weight
1 – draw the axes and decide which variable goes on which axis Hours per week on Facebook Quality of Facebook relationships

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2 – determine the range of values to use for each variable and mark them on the axes Hours per week on Facebook Quality of Facebook relationships 2 4 6 8 10 14 12 18 16 20 0 1 2 3 4 5
3 – Mark a dot for each pair of scores Hours per week on Facebook Quality of Facebook relationships 2 4 6 8 10 14 12 18 16 20 0 1 2 3 4 5 Hrs Rate 10 5 20 4 5 3 2 1

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Scatter Diagram Hours per week on Facebook Quality of Facebook relationships 2 4 6 8 10 14 12 18 16 20 0 1 2 3 4 5 Hrs Rate 10 5 20 4 5 3 2 1
Draw a line that best represents the dots Hours per week on Facebook Quality of Facebook relationships 2 4 6 8 10 14 12 18 16 20 0 1 2 3 4 5 Hrs Rate 10 5 20 4 5 3 2 1

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Line graphs Linear (straight line) Curvlinear (U-shaped) Good for predictions
Regression (Prediction) Line Slope: how steep the line is and in what direction When using z-scores, slope = correlation Y-intercept: where the line crosses the y- axis; value of Y when X=0

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Vocabulary Predictor (X) Criterion (Y) Regression Coefficients (B and β) Standardized: from z-scores, Betas Unstandardized: from raw scores Proportion of variance accounted for aka Coefficient of determination

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Prediction Question: How much will the LOST audience enjoy THE EVENT? ?
NBC’s Focus Group? To what extent did you enjoy watching LOST? To what extent did you enjoy watching the premiere of THE EVENT? 1 = a little enjoyment 2 = some enjoyment 3 = enjoyment 4 = much enjoyment 5 = a lot of enjoyment

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X = LOST enjoyment Y = THE EVENT enjoyment 1 2 1 3 2 1 3 4 3 5 4 5 4 3 4 2 4 1 5 4
X-M -2.1 -2.1 -1.1 -0.1 -0.1 0.9 0.9 0.9 0.9 1.9 Y-M -1 0 -2 1 2 2 0 -1 -2 1 (X-M)(Y-M) 2.1 0 2.2 -0.1 -0.2 1.8 0 -0.9 -1.8 1.9 ∑(X-M x )(Y-M Y ) = 5, n = 10 Covariance = .5

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X-M -2.1 -0.1 -0.1 0.9 0.9 1.9 Y-M -1 1 2 2 -2 1 (X-M)(Y-M) 2.1 1.8 Below the mean on X (negative) Below the mean on Y (negative) Negative times Negative = Positive (a match!) Above the mean on X (positive) Above the mean on Y (positive) Positive times Positive = Positive (a match!)
X-M -2.1 -2.1 -1.1 -0.1 0.9 0.9 0.9 1.9 Y-M -1 0 -2 1 0 -1 -2 1 (X-M)(Y-M) 2.1 0 2.2 -0.1 -1.8 1.9 Below the mean on X (negative) Above the mean on Y (positive) Positive times Negative = (NO match!) Above the mean on X (positive) Below the mean on Y (negative) Negative times Positive = (NO match!)

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Match or No Match? Match + Neither Match + No Match - No Match - Match + Neither No Match - No Match - Match + Extent of Match large large small small large small large large (X-M)(Y-M) +2.1 0 2.2 -0.1 -0.2 +1.8 0 -0.9 -1.8 +1.9 Taken all together, the matches are larger than the non-matches, so a positive covariance
Covariance to Correlation Can’t compare covariance across studies Covariance dependent on variance of X and variance of Y Standardize covariance – put covariance on a common metric Standardize by dividing by standard deviations ( 29 ( 29 ) )( )( ( ] [ Y X Y X s s N M Y M X - -

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Covariance to Correlation 272 .
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## This note was uploaded on 05/26/2011 for the course PSCH 343 taught by Professor Victoriaharmon during the Spring '11 term at Ill. Chicago.

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(Exam 2) SimpleRegression 11 - Simple Linear Regression...

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