Notes 5

# Notes 5 - Notes 5 Regression Scatterplotnow what We next...

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Regression Scatterplot…now what? We next attempt to establish some relationship between the explanatory variable X and the response variable Y. A straight line of the form Y = mX + c , where m = gradient and c = y-intercept, will be used to relate the variables X and Y . Having an equation relating X and Y would allow us to make predictions for the response Y given some value of X . : It is only natural that our prediction for the response of the mean of x should be mean of y and so our curve should pass through the center (centroid) of the data set, ( x , y ). Fitting a straight line to data is called Linear Regression Analysis and the straight line is referred to as the regression line . LSR is a computational method that finds the “best fit” curve (model) that passes through the centroid ( x , y ) of the data set while having the smallest error between this estimated curve and the actual data points. To minimize error, the curve/line must pass as close as possible to points on the scatterplot. This “closeness” is measured by looking at the residuals. (Note : Linear Regression (Straight lines) is the focus in this course.) The difference between the observed data value of y and our predicted value for y, known as y ˆ is called the residual, denoted by e . There is a residual for each y in our data. Residual:

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Notes 5 - Notes 5 Regression Scatterplotnow what We next...

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