CHarris - MAT 243 Project Three Summary Report

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Southern New Hampshire University *

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APPLIED ST

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Mathematics

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Feb 20, 2024

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MAT 243 Project Three Summary Report Chanelle Harris Chanelle.harris@snhu.edu Southern New Hampshire University

As we continue to advance and improve our team, we have been tasked to continue our analysis. We have been asked to come up with regression models that predict the number of wins in a regular game based on the performance metrics that are included in each data set. These regression models will help us take the total number of wins, average points scored, average relative skill and the average point differential between our team and our comparison team to make key decisions to improve the performance of the team. We will use variables like the average points differential to compare the differences between our team's and the opponent’s average points in a regular season by subtracting the points the Cavs scored from those the Chicago Bulls scored. We will also use the average relative skills, which is the average team’s skill level in a regular season. This is calculated by using the team’s final score, the game location, and the outcome of the game relative to the probability of that outcome. To study the correlation of our variables we have built a scatterplot of the total number of wins versus the average relative skill. Using data visualizations tools, we can see the relationship between the two variables. Components like the correlation coefficient is used to describe the strength and the direction of the association. As shown in the chart above, our correlation is 0.9072 and features a strong positive correlation. We are looking at this with a 1% level of confidence and our chart shows us that we have a p-value equal to 0, which since it is less than 1% this tells us that this graph is statistically significant. We use the simple linear regression to predict the value of an output variable, known as the response, based on the value of an input variable, called the predictor. This is to model the relationship between two continuous variables. The model equation to find the total number of wins is y= α + β x. The null hypothesis equation is H 0 : β1 = 0, which tells us that there is no correlation existing between number of wins and the high average points in a season. The alternative hypothesis equation is H α : β1 ≠ 0, which we are saying that the

number of wins in a season does correlate with the high average points in a season. We will be using a level of significance at 1% or 0.01. Table 1: Hypothesis Test for the Overall F-Test Statistic Value Test Statistic 2865.00 P-value 0.00 Immediately looking at this chart we know that since our p-value is less than 0.01, or 1%, that there is significant evidence to reject our null hypothesis. Proving that there is a correlation between our team’s number of wins and the average points per season. We use this model to predict the total number of wins in a regular season for a team based off the relative skill level. For example, if the relative skill level is 1550 then the equation reads as is total_wins = -128.2475 + (0.1121(1550)) = 45.5, or if the relative skill is 1450, then the equations read: total number of wins = -128.2475 + (0.1121(1450)) = 34.2. To show the linear relationship between a response variable and two or more predictor variables we will use the multiple linear regression model. The standard equation for the model is Y = β0 + β 1 X 1 + β 2 X 2. Using the data that we pulled for our team, our equation is Y = -152.5736 + 0.3497(avg_pts) + 0.1055(avg_elo_n). The null hypothesis (H 0 : β 1 = β 2 = 0) states that there is no relationship between the response variable and any of the predictor variables. The alternative hypothesis (Hα: At least one βi ≠ 0 for i = 1, 2) states a relationship exists with at least one variable. The level of significance we are using is 1% or 0.01.

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