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Regression Paper
According to Doane and Seward (2007), “Bivariate regression is a flexible way of analyzing relationships between two quantitative variables” (page 500). Team B is using the baseball data set to determine if the number of stolen bases by each Major League Baseball (MLB) team has a direct connection with the amount of games won by each team. In order to determine if there is a relationship between stolen bases and wins, Team B will develop a hypothesis, perform the regression hypothesis test using the fivestep procedure for hypothesis testing, and interpret the results of the test. Hypothesis Statements In using the baseball data set there is a fair amount of statistics to go through to formulate a hypothesis. MLB teams are always looking for ways to improve their win to loss ratio so they could use the data set to determine factors that are being overlooked. For the purpose of this assignment, Team B will look at the number of stolen bases each MLB team had during the 2005 season and compare them to the number of wins using linear regression analysis to determine whether there is a significant relationship between these two variables. When working with linear regression analysis, the dependant variable needs to have a linear relationship with the independent variable. In this experiment, the dependant (Y) variable is the number of stolen bases and the independent (X) variable is the number of wins for the respective teams. The hypotheses for the data set are: H₀: p = 0 (There is correlation between number of wins and number of stolen bases) H₁: p ≠ 0 (There is no correlation between number of wins and number of stolen bases) Regression Hypothesis Test A regression hypothesis test is done in the same manner as other hypotheses tests. Team B will first state the hypothesis, select a level of significance, identify the test statistic, state the decision rule, and take a sample and arrive at a decision. Major League Baseball teams are always looking for ways to improve performance, so Team B wants to determine if the amount of stolen bases and team wins are in any way related. The level of significance Team B will use is α = .05. The test statistic is 1.269. The critical value is 2.048. The p value for the regression line is .2149, which is more than .05. The regression line for the baseball data is y = 28.31 + 0.7059x. The meaning of the regression line is that every stolen base will add .7059 wins for the team. Results of the Regression Hypothesis Test The linear regression analysis Team B used shows there is a relationship between stolen bases and wins. Though the relationship is not very strong, as the lower confidence level is .04335 and the upper confidence level is 1.8454. r = 0.233 showing signs of a positive relationship between the variables. Linear regression is an approach to modeling the relationship between a variable denoted Y and one or more variables denoted X. In this case, MLB wins equals 28.31 plus .7059 times the number of stolen bases. In linear regression, models of the unknown parameters are estimated from the data using linear functions. Taking a random couple of teams to test the model Team B compared the Minnesota Twins and New York Yankees and came up with 100.3118 = 28.31 + 0.7059(102) for Minnesota and 87.60 = 28.31 + 0.7059(84) for New York. Minnesota had 83 regular season wins and the Yankees had 95 wins, this shows the relationship between the two is not extreme. Minnesota had 18 more stolen bases than New York, but New York had 12 more wins than Minnesota. The overall average of teams with a higher level of stolen bases produced more wins, despite this example. The results of the linear regression analysis show that there is a correlation between stolen bases and wins for Major League Baseball teams. This holds true from a baseball standpoint as stolen bases are helpful but not essential in playing winning baseball. Conclusion For the regression paper, Team B wanted to determine if there was a connection between the amount of stolen bases and games won by the teams in MLB. Team B performed a regression analysis test on the MLB 2005 data and determined there is a weak positive relationship between the amounts of stolen bases and wins. The value of r = .233 which is more than zero and less than one. The rvalue is a weak positive that there is a linear relationship between total number of wins by each team and the number of stolen bases by each team. The test statistic is less than the critical value and the p value is more than .05 so Team B concludes there is a relationship between stolen bases and total wins in MLB and accepts the null hypothesis. http://www.oppapers.com/essays/Regression/380519 