or major league baseball teams, do higher player payrolls mean more gate money? Here are data for each of the National League teams in the year 2002 . The variable x denotes the player payroll (in millions of dollars) for the year 2002 , and the variable y denotes the mean attendance (in thousands of fans) for the 81 home games that year. The data are plotted in Figure 1 scatter plot, as is the least-squares regression line. The equation for this line is =y+5.910.34x . Answer the following: 1. Fill in the blank: For these data, mean attendance values that are less than the mean of the mean attendance values tend to be paired with player payroll values that are _____ the mean of the player payroll 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 0.34 thousand fans in mean attendance. Choose oneincreasedecrease 3. From the regression equation, what is the predicted mean attendance (in thousands of fans) when the player payroll is 103.5 million dollars? (Round your answer to at least two decimal places.) 4. What was the observed mean attendance (in thousands of fans) when the player payroll was 103.5 million dollars?

1. Fill in the blank: For these data, mean attendance values that are less than the mean of the mean attendance values tend to be paired with player payroll values that are _____ the mean of the player payroll 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 0.34 thousand fans in mean attendance.	Choose oneincreasedecrease
3. From the regression equation, what is the predicted mean attendance (in thousands of fans) when the player payroll is 103.5 million dollars? (Round your answer to at least two decimal places.)
4. What was the observed mean attendance (in thousands of fans) when the player payroll was 103.5 million dollars?

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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