For major league baseball teams, do higher player payrolls mean more gate money? Here are data for each of the American League teams in the year 2001 . The variable x denotes the player payroll (in millions of dollars) for the year 2001 , and the variable y denotes the mean attendance (in thousands of fans) for the 81 home games that year. The data are plotted in the Figure 1 scatter plot, as is the least-squares regression line. The equation for this line is =y+13.820.23x . Player payroll, x (in $1,000,000s) Mean attendance, y (in thousands) Anaheim 46.6 24.69 Baltimore 73.4 38.15 Boston 109.6 32.47 Chicago White Sox 62.4 21.85 Cleveland 92.0 39.26 Detroit 49.8 23.70 Kansas City 35.6 19.01 Minnesota 24.4 21.98 New York Yankees 109.8 40.25 Oakland 33.8 26.54 Seattle 75.7 43.33 Tampa Bay 55.0 16.05 Texas 88.5 34.94 Toronto 75.8 23.70 y 5 10 15 20 25 30 35 40 45 x 20 40 60 80 100 120 140 0 Figure 1 Answer the following: 1. Fill in the blank: For these data, player payroll values that are greater than the mean of the player payroll values tend to be paired with mean attendance values that are _ the mean of the mean attendance values. Choose onegreater thanless than 2. Fill in the blank: According to the regression equation, for an increase of one million dollars in player payroll, there is a corresponding _ of 0.23 thousand fans in mean attendance. Choose oneincreasedecrease 3. What was the observed mean attendance (in thousands of fans) when the player payroll was 109.8 million dollars? 4. From the regression equation, what is the predicted mean attendance (in thousands of fans) when the player payroll is 109.8 million dollars? (Round your answer to at least two decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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For major league baseball teams, do higher player payrolls mean more gate money? Here are data for each of the American League teams in the year

2001

. The variable

denotes the player payroll (in millions of dollars) for the year

2001

, and the variable

denotes the mean attendance (in thousands of fans) for the

home games that year. The data are plotted in the Figure 1 scatter plot, as is the least-squares regression line. The equation for this line is

=y+13.820.23x

	Player payroll, x (in $1,000,000s)	Mean attendance, y (in thousands)
Anaheim	46.6	24.69
Baltimore	73.4	38.15
Boston	109.6	32.47
Chicago White Sox	62.4	21.85
Cleveland	92.0	39.26
Detroit	49.8	23.70
Kansas City	35.6	19.01
Minnesota	24.4	21.98
New York Yankees	109.8	40.25
Oakland	33.8	26.54
Seattle	75.7	43.33
Tampa Bay	55.0	16.05
Texas	88.5	34.94
Toronto	75.8	23.70

100

120

140

Figure 1

Answer the following:

1. Fill in the blank: For these data, player payroll values that are greater than the mean of the player payroll values tend to be paired with mean attendance values that are _____ the mean of the mean attendance values.	Choose onegreater thanless than
2. Fill in the blank: According to the regression equation, for an increase of one million dollars in player payroll, there is a corresponding _____ of 0.23 thousand fans in mean attendance.	Choose oneincreasedecrease
3. What was the observed mean attendance (in thousands of fans) when the player payroll was 109.8 million dollars?
4. From the regression equation, what is the predicted mean attendance (in thousands of fans) when the player payroll is 109.8 million dollars? (Round your answer to at least two decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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