MAT 243 Project Three

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Southern New Hampshire University *

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243

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Mathematics

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Apr 25, 2024

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docx

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MAT 243 Project Three Summary Report Stewart Meece Stewart.meece@snhu.edu Southern New Hampshire University
1. Introduction The data set I am exploring is NBA wins with the average point scored, average relative skill, and average point differential between the team and their opponent in the regular season. My results will be used to predict the total number of wins for a team in a regular season based on past performance metrics. I will be running a multiple linear regression analysis to calculate the request information the coach has requested. This is the predicted total number of wins of a team for a regular season. 2. Data Preparation Looking at the variables that we were given, we know that ‘avg_pts_differential’ represents the overall difference in average points between the two teams in the regular season. What this shows is the difference in points scored between our team and the opposing team. An example of this would be if our designated team were to score an average of 96 points, and the opposing team were to score an average of 90 points, then the average point differential would be +6. The reason for the number being positive is that we would have to take the difference between both teams average scores. The variable that is labeled as ‘avg_elo_n’ represents the average points scored by each team in a regular season. How this is calculated is based on the final score of the game, the location of the game, and the overall outcome of the game relative to the probability of the outcome. As the number increases, the higher the relative skill of that team. This also means that the team with a higher relative skill level is assumed to win a game against a team that has a much lower relative skill level.
3. Simple Linear Regression: Scatterplot and Correlation for the Total Number of Wins and Average Relative Skill We typically see data visualization as all of the raw data and models and deliver them in a way that we can formulate conclusions regarding it. What this accomplishes is that we can see the areas that we need to improve upon and we can communicate this information in a way that is fast and effective. The correlation coefficient is used to determine the strength and direction of two variables by understanding where they come from. All forms of correlation, such as weak, moderate, and strong, all depend on a value. Anything below 0.40 will indicate a weak correlation, anything between 0.40 and 0.80 will represent a moderate correlation, and anything between 0.80 and 1.0 will indicate a strong correlation. If both of the variables are shown to increase, then that results in a positive correlation. Likewise, if the variables were to decrease, then the correlation would be negative. Since the scatterplot and the Pearson correlation coefficient both show a positive correlation between total number of wins and the average number of points scored, we can conclude that this will result in a moderate correlation due to the correlation coefficient value, which is 0.4777. Likewise, the correlation coefficient is statistically significant with a P-value of 0.0.
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