{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L choose values that give the best fit l what do you

Info iconThis preview shows pages 20–29. Sign up to view the full content.

View Full Document Right Arrow Icon
l Choose values that give the best fit l What do you mean best fit? l One approach is minimize residual sum of squares l Method called least squares l Basis of regression analysis (see Keller Ch 16)
Background image of page 20

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
21 Least squares: The diagram x b b y 1 0 ˆ + = y x w w w w b 0 e 1
Background image of page 21
22 Least squares: The optimization problem squares of sum residual the minimize that estimates slope and intercept be will solution Thus ) ˆ minimize to chosen are where ˆ Assume 2 1 1 0 1 0 i i n i i i y y ( b b x b b y - + = =
Background image of page 22

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
23 Least squares: The solution x b y b s s b x xy 1 0 2 1 - = = l Note: l Point of the means will lie on line of best fit l b 1 will have same sign as covariance (correlation) between l Zero covariance (correlation)  b 1 = 0  ?
Background image of page 23
24 Internet use: Keller exercise 3.52 and extension l Problem l Interested in internet usage l l Data l Random sample of 15 adults l Two variables l Education (years) l Internet use (hours in previous week) l What are the key features of these variables & their relationship?
Background image of page 24

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Internet use: Excel summary statistics 25 Education Internet use Mean 12.667 Mean 10.000 Standard Error 0.779 Standard Error 1.857 Median 11 Median 10 Mode 11 Mode 0 Standard Deviation 3.016 Standard Deviation 7.191 Sample Variance 9.095 Sample Variance 51.714 Kurtosis -0.114 Kurtosis -0.432 Skewness 0.586 Skewness 0.181 Range 11 Range 24 Minimum 8 Minimum 0 Maximum 19 Maximum 24 Sum 190 Sum 150 Count 15 Count 15
Background image of page 25
26 Internet use: Scatter diagram & fitted regression line 0 5 10 15 20 25 30 0 2 4 6 8 10 12 14 16 18 20 Hours of use Education Internet use
Background image of page 26

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
27 Internet use: Regression line l b 1 = 15.296/(9.095) = 1.682 b 0 = 10 – 1.682*12.677 = – 11.323 l Be careful: EXCEL uses population formulae in calculating covariances = 15.296 = 14.267*(15/14) l See Keller p. 138 Covariance Education Internet use Education 8.489 Internet use 14.267 48.267 Correlation Education Internet use Education 1 Internet use 0.705 1
Background image of page 27
28 Internet use: Summary
Background image of page 28

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Progress report #1 l Descriptive statistics (Emphasis of course so far) l What are the key features of data? l How can we best describe these features so that analysis is informative l Inferential statistics (Emphasis of course to come) l Extracting information about population parameters on basis of sample statistics l What does a sample mean tell us about a population mean? l Typically only alternative because difficult or impossible to determine population mean l Need more foundations before covering later in course 29
Background image of page 29
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page20 / 29

l Choose values that give the best fit l What do you mean...

This preview shows document pages 20 - 29. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online