Basic Business Statistics, Student Value Edition

14th Edition

ISBN: 9780134685113

Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat

Publisher: PEARSON

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Chapter 14, Problem 73PS

Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (Shots made) percentage and three-point goal percentage for a recent season. The data stored in NBA.

a. State the multiple regression equation.

b. Interpret the meaning of the slopes in this equation.

c. Predict the mean number of wins for a team that has a fields goal percentage of 45 % and a three-point field percentage of 35 % .

d. Perform a analysis on your model and determine whether the regression assumptions are valid.

e. Is there a significant relationship between the number of wings and two independent variables (field goal percentage and three-point field goal percentage) at the 0.05 level of significance?

f. Determine the p-value in (e) and interpret is meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted r 2 .

i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

j. Determine the p-value in (i) and interpret their meaning.

k. Compute and interpret the coefficients of partial determination.

l. What conclusions can you reach concerning field goal percentage and three-point goal percentage in predicting the number of wins?

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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Chapter 14, Problem 72PS

Chapter 14, Problem 74PS

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