Ch. 10 Correlation and Regression 10-2 Notes Linear Regression and the Coefficient of Determination.

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Ch. 10 Correlation and Regression 10-2 Notes Linear Regression and the Coefficient of Determination

What criterion do we use to establish what is the “best fit” line? Least Squares Criterion – The line we fit to the data must be such that the ______ of the ___________ of the ____________________ from the ________ to the ______ be made _____________________ __________. Activity least squares

Tech Notes To find lr equation using TI 83/84 Use STAT, CALC, option 8:LinReg(a+bx), the value of a and b will be given. Let x be the number of ads run in a given week and y be the number of cars sold that week. Ex. X Y

Making Predictions using the linear model equation Predicting for x values ___________ observed x values is called ________________. Predicting for x values ___________ observed x values is called _________________. Any prediction using the lr equation as a model will carry with it some _______________. The better the data ________________, the more accurate the ________________ will be. Also, making ________________ can be quite risky. It assumes the model holds true beyond the data, which may not be valid and therefore produce ____________ _______________.

Using the least squares equation from before, to predict the number of car sales for a week when 12 ads were run. Predict the number of cars expected to be sold if 50 ads were sold. What concerns might you have?

Coefficient of Determination (r 2 ) – the ratio of explained variation over total variation. In other words the amount of variation in y that can be explained by the change in the x-value using the linear regression equation. The other portion of variation is due either to chance or outside factors.

Ex. 1 The number of workers on an assembly line varies due to the level of absenteeism on any given day. In a random sample of production output from several days of work, the following data were obtained, where x = number of workers absent from the assembly line and y = number of defects coming off of the line. x35021 y a) Draw a scatter diagram for the data

b) Find the equation for the least-squares line (lr) to c) sketch the least squares line on the scatter diagram d) On a day when 4 workers are absent from the assembly line, what would the least- squares line predict for the number of defects coming off the line? e) find the value of the coefficient of determination r 2. Explain its meaning in context.

Assignment Day 1 p. 520 #1, 3, 4, 9, 11, 15 Day 2 p. 520 #5, 8, 12, 13, 14, 17, 18

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