lec9 - STATISTICS 13 STATISTICS Lecture 9 Oct. 15, 2010...

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STATISTICS 13 STATISTICS 13 STATISTICS 13 Lecture 9 Lecture 9 Oct. 15, 2010 Oct. 15, 2010
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Review Box plot Comparative pie charts and bar charts Scatter plot Pattern, direction Strength Unusual observations?
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Numerical Measures for Two Quantitative Variables Measures to describe : Strength (strong/weak) and direction (positive/negative) of the relationship Form or description (linear/curvy) of the relationship
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Correlation Coefficient Correlation coefficient r: Measures the strength and direction of the linear relationship between X and Y y x xy s s s r s x = standard deviation of the x ’s s y = standard deviation of the y ’s s x = standard deviation of the x ’s s y = standard deviation of the y ’s where 1 ) )( ( 1 ) )( ( n y y x x n n y x y x s i i i i i i xy
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Interpreting r -1 r 1 r 0 r 1 or –1 r = 1 or –1 Sign of r indicates direction of the linear relationship. Positive means Y increases with increasing X . Weak linear relationship; random scatter of points, or other nonlinear relationship Strong linear relationship; either positive or negative All points fall exactly on a straight line.
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Example: Psychological Reports Expenditures Per Capita GDP per Capita 83.53 18,045.00 1507298.85 71.38 14,449.80 1031426.72 64.79 19,842.15 1285572.90 41.21 17,670.15 728186.88 9.17 7,563.70 69359.13 54.98 19,763.63 1086604.38 325.06 97334.43 5708449 i X i Y i i Y X sum: 1 ) )( ( n n y x y x s i i i i xy y x xy s s s r
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Example : Airline Passenger Booking vs. Hotel Occupancy Data on the airline passenger booking and hotel occupancy rate near Orlando, Florida X = thousands of passengers booked for airline flights by Eastern Airlines to Orlando International Airport Y = occupancy rate for Walt Disney World area hotels (in %) X 65.7 71.6 53.7 70.2 75.0 85.6 84.6 58.0 72.8 87.6 85.4 50.6 Y 40 41 48 49 73 74 68 51 63 75 70 38 (Source : Florida Department of Business Regulation, Orlando Area Chamber of Commerce, and Finance Dept. of Orlando International Airport)
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Calculation of Correlation Passenger Occupancy 90 80 70 60 50 40 Scatterplot of Occupancy vs Passenger
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Property of Correlation Coefficient Correlation coefficient is a pure number without any unit
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lec9 - STATISTICS 13 STATISTICS Lecture 9 Oct. 15, 2010...

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