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# EXAM REVIEW REGRESSION AND CORRELATION.doc

7 Pages
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School
University of Toronto Scarborough
Department
Psychology
Course
PSYB07H3
Professor
Douglas Bors
Semester
Fall

Description
30 STRAIT STTC MARK 30 STRAIT STTC MARKAFTER MIDTERM EXAM NOTES REGRESSION AND CORRELATION Relation between Two Variables Regression and Correlation: In both cases, y is a random variable beyond the control of the experimenter. In the case of correlation, x is also a random variable. In the case of regression, x is treated as a fixed variable. (As if there is no sampling error in x.) Regression: you are wishing to predict the value y on the basis of the value of x -how change are we to expect with a change in 1 variable  to put into units of measurement -i.e. predicting final mark based on midterm mark Correlation: you are wishing to express the degree of the relation between x and y -like the phi coefficient  degree of relation between the two variables -how good/how much error in the prediction? -if x and y are unrelated, the best predictor of y is the mean of y -you have to look for something that minimizes the error Scatter Plot -X axis (abscissa) = predictor variable -Y axis (ordinate) = criterion variable Example: GPA vs. statistic mark: Positive Negative Perfect None -linear relationship always but there are non relationship forms of regression and correlation -the denomination of positive, negative etc, has nothing to do with the quality of the relation -Positive: (+) changes in one variable leads to (+) change in second variable-Negative: (+) changes in one variable leads to (-) changes in second variable (?) -Perfect: change in produces predicted changes in y Covariance -is a number reflecting the degree to which two variables vary or change in value together (x − x) y −(y) C x =yO V n −1 n= the number of xy pairs Example: collecting reaction time and error scores -If a subject is slow (high x) and accurate (low y), then the d score for the x will be positive and the d score for the y will be negative; their product will be negative. -If a subject is slow (high x) and inaccurate (high y), then the d score for the x will be positive and the d score for the y will be positive; their product will be positive. -If a subject is fast (low x) and accurate (low y), then the d score for the x will be negative and the d score for the y will be negative; their product will be positive. -If a subject is fast (low x) and inaccurate (high y), then the d score for the x will be negative and the d score for the y will be positive; their product will be negative. **d score = deviation score (score minus mean)Scatter plots of the data: There is a trend after all -There is no linear relationship between x and y but a perfect relationship -always look/draw scatterplot to make conclusions on trends • Scale issues Example: i.e. using minutes vs. seconds (Sec.) (Min.) -the absolute value of the covariance is a function of the variance of x and the variance of y thus, a covariance could reflect a strong relation when the two variance are small, but maybe express a weak relation when the variance are large For a perfect relationship: -linear relation is one in which the relation can be most accurately represented by straight line -linear transformation is represented by: x = c (x ) + c n e 1 w o l d2 -general equation for a straight line: y = bx + a  a is the y intercept and b is the slope Δy
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