110_lec12and13_Simple_Linear_Regression

110_lec12and13_Simple_Linear_Regression - Simple Linear...

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Simple Linear Regression Professional Golfer's Putting Success Rates 0 10 20 30 40 50 60 70 5 7 9 11 13 15 17 Distance of Putt in feet Percentage of success Regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We use a regression line to predict the average value of the response variable y for a given value of x .
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Least-Squares Regression Line The least-squares regression line is the line that makes the vertical distances of the data points from the line as small as possible. Professional Golfer's Putting Success Rates 0 10 20 30 40 50 60 70 5 7 9 11 13 15 17 Distance of Putt in feet Percentage of success
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Least-Squares Regression Line The equation of the line takes the form y = a + bx Where b is the slope (the amount by which y changes when x increases 1 unit) of the line and a is the y- intercept (value of y when x = 0). Professional Golfer's Putting Success Rates 0 10 20 30 40 50 60 70 5 7 9 11 13 15 17 Distance of Putt in feet Percentage of succes Success Rate = 82 – 4.5(Distance)
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Least-Squares Regression Line Success Rate = 82 – 4.5(Distance) y = 82 – 4.5 x For every increase of 1 foot in distance, the success rate goes down by 4.5%. At a distance of 0 feet, the success rate is 82% (does that make sense?) Use the regression equation to predict the average success rate at 10 ft.; 12 ft; 2 ft.
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Prediction is based on fitting some “model” to a set of data. Model is the form – straight line or curve. Prediction works best when the model fits the data closely. Prediction outside the range of the available
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110_lec12and13_Simple_Linear_Regression - Simple Linear...

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