STAT141 Chapter Notes - Chapter 8&9: Scatter Plot, Standard Deviation

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Idea: fit a straight line through the data to predict the values of response (y) at specified values of x. Least squares regression line (yhat): a straight line that describes relationship between one dependent and one independent variable when they follow a linear pattern, where yhat = b0 + b1x. Residuals (ei) or error of prediction (y yhat): vertical distance from a point (x, y) to (x, yhat) (underestimate) Positive residue: y > yhat; observed is greater than prediction. Negative residue: y < yhat; observed is less than prediction (overestimate) Sum of the residuals is always 0. Slope of yhat: moving one standard deviation away from the mean of x moves r standard deviations away from the mean of y, where slope = b1 = r(sy /sx) Lurking variables: third variable; may falsely suggest a strong relationship between x and y. No matter how large r2 value or how straight the line, association does not imply causation.

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