Ch. 10 Correlation and Regression

10-2 NotesLinear 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

http://www.explorelearning.com

Tech NotesTo find lr equation using TI 83/84Use 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 6 20 0 14 25 16 28 18 10 8

Y 15 31 10 16 28 20 40 25 12 15

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 (r2) – 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.

x 3 5 0 2 1

y 16 20 9 12 10

a) Draw a scatter diagram for the data

b) Find the equation for the least-squares line (lr) to 0.001.

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 r2 . 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