EDP 660 LEAST SQUARES HANDOUT EDP 660 LEAST SQUARES HANDOUT In a very small scale study of persistence, an experimenter gave three subjects a very difficult task. Data on the age of the subject (X) and on the number of attempts to accomplish the task before giving up (Y) follow:Subject i 1 2 3Age Xi20 55 30Number of attempts Yi5 12 10To find “good” estimators of the regression parameters β0 (y-intercept) and β1 (slope), first graph the sample data as a scatterplot.Filling in the table below, we will calculate the line (iixy10ˆˆˆ) through the above points for which the SSE is a minimum (least squares line, regression line, or least squares prediction equation.) xyxy)( xx 2)( xx ))(( xxyy Σ = Σ= Σ=Now calculate the following using the values from the table:y-intercept: xy10ˆˆslope: 21)())((ˆxxxxyySo, the least squares line for these data is (write the formula for the line, and draw it in the plot above):Now using that formula, calculate the following:xyyˆyyˆ2)ˆ( yy Σ= Σ= Σ=Finally, define the following terms, then fill in the above dialogue boxes:SSxx
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