project 3 math 243
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Southern New Hampshire University *
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243
Subject
Mathematics
Date
Jan 9, 2024
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docx
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10
Uploaded by melgal14
Mat-243 Project 3 Summary Report
Melissa Galvan
Melissa.galban@snhu.edu
Starting point The average points scored, average point difference, average relative skill, and the overall number of wins for our team and the opposition during the regular season will be the data sets I will be investigating or exploring in this study. Utilizing this data will allow us to evaluate our team's performance in the upcoming playing season and possibly forecast it. We anticipate that this data set should accurately reflect our team's performance in terms of the number of victories determined by the measured data. 1. preparing data
We'll use a variable called "avg_pts_differential" to show the average number of points our team and its opponents had during the season. This statistic will be used to determine the variance in points scored during play by both our team and our opponents. We could use the following example for someone who wouldn't understand this: The average point differential would be +4 if our team's average point total was 121 and the other team's average point total
was 125. Because of the gap in point averages between our side and the opposition, we would like a positive figure. Use a multiple linear regression analytical method to evaluate data that the coaches and higher management of our team will use. The relative skill of each team during the regular season would be highlighted by another variable we'd use. The name of this variable would be "avg_elo_n". This measurement is based on the location of the game, the outcome of the match in relation to the probability of a particular outcome, and the
final score of the match. also the final result. The quantity will be higher when a team has a high level of relative skill. It is predicted that a team with a higher relative skill will win over a team with a lower or lessened relative skill.
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2. Scatterplot and Correlation for Average Points Scored and Total Number of Wins Data visualization uses a diagram, chart, or image to visually represent data or information. To explore the link between the data or information on the forms mentioned above, data visualization techniques are used. A negative association between two variables is indicated when the data is distributed in a way that one variable rises while the other falls. Both variables have a positive connection if they both rise in value. There would be no association between the two variables if the data were distributed randomly with no trends or patterns. The range of the coefficient of correlation's parameters is from -1 to +1. The correlation coefficient value indicates with a positive or negative symbol the direction of the association between two variables. The correlation coefficient's value indicates how strongly the two variables being used are related. There would be no association between the two variables if the value were 0. A negative absolute relationship between two variables would be represented by the number -1. +1, on the other hand, denotes a completely positive affiliation
between two variables. The scatterplot shown below demonstrates how the given data is distributed in an increasing way. As the average points scored value grows, so does the value of the overall number of wins. This suggests that the two variables are positively related. The value of the Pearson correlation coefficient is 0.9072. As the average number of points scored changes in value, so does the value of the overall number of victories. The results of the scatterplot indicate a p-value of 0. If the p-value is less than 0.05, there is no association between the two variables, according to our significance level of 0.01.
Correlation between Average Relative Skill and Total Number of Wins:
Pearson Correlation Coefficient = 0.9072
p-value = 0.0000
3: Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill
The link between the single response variable and the predictor variable is estimated using a straightforward linear regression. The link between the variables will be described using the regression analysis. The model's equation is as follows: (Y) = βo + β1X1. Bo will stand in for the
overall winning percentage, and B1 will stand in for the typical points scored. The total F- test scores are as follows:
a. The null hypothesis, which is comparable to zero, represents the average number of points scored. The null hypothesis does not hold any weight. According to statistics, it is as follows: ( β1 = 0 )
b. The alternative hypothesis does not equate to zero and instead shows the average points scored. It is statistically notated as (1 0) and has a significance.
4: Scatterplot and Correlation for the Total Number of Wins and Average Points Scored
The link between the single response variable and the predictor variable is estimated using a straightforward linear regression. The link between the variables will be described using the regression analysis. The model's equation is as follows: (Y) = βo + β1X1. Bo will stand in for the
overall winning percentage, and B1 will stand in for the typical points scored. The total F- test scores are as follows: a. The null hypothesis, which is comparable to zero, represents the average number of points scored. The null hypothesis does not hold any weight. According to statistics, it is denoted as (1 = 0).
b. The alternative hypothesis does not equate to zero and instead shows the average points scored.
c. 1% of the data are significant.
e. The p-value of 0.00 indicates that we should reject the null hypothesis and accept the alternative one. Since there is a clear correlation between average points scored and total wins, average points can predict the number of victories. If a team averaged 75 points per game during the regular season, they should win 12 games overall. A club that averaged 90 points per game during the regular season would likely play in 30 games.
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Correlation between Average Relative Skill and Total Number of Wins Pearson Correlation Coefficient = 0.9072
P-value = 0.0
5. Multiple Regression: Predicting the Total Number of Wins using Average Points Scored and Average Relative Skill
Using a large number of predictor variables, or multiple predictor variables, a multiple linear regression model is used to examine and forecast a response variable by exercising the entire regression function population and the regression error. The model's equation is as follows: Y = o
+ 1X1, 2X2,.. -152.5736 + 0.3497 (X1), 0.1055 (X2)
ɛ
a. The model is not usable, according to the null hypothesis. All slope parameters also have a value of zero. In statistics, the null hypothesis is denoted as follows:Ho: β1 = β2 = 0
b. According to the other theory, at least one parameter is not equal to zero. According to statistics, it is as follows: H2: β1 ≠ 0
c. The significance level is 0.01 or 1%d. e. As a result of this test, the null hypothesis should be disregarded because the p-value is 0.00. It
implies that at least one parameter is not comparable to zero. In contrast, it is correlated with the response variable. A minimum of one predictor variable is statistically significant for predicting the number of victories, according to the findings of the complete F-Test. Since the p-
value for the t-test was less than 1%, we may conclude that all of the predictors are statistically significant. The following variables were tested using a t-test:7.297 is the average, or 0.3497 / 0.048. Skill ratio average: 0.1055/0.002 = 47.952. The correlation coefficient is equal to 0.837, or 83.7%.
6: Multiple Regression: Predicting the Total Number of Wins using Average Points Scored, Average Relative Skill, Average Points Differential and Average Relative Skill Differential
By testing the whole population of the regression function and the regression error, a multiple linear regression model is used to examine and forecast a response variable using many, or multiple, predictor variables. This model's equation is written as Y = o + 1X1 + 2X2 +
.a. It states that the model cannot be used in relation to the null hypothesis. Additionally, all slope
parameters are equal to zero, and there is no statistically significant correlation between the predictor and responder variables. According to statistics, it is as follows: Ho: β1 = β2 = 0 b.
c. Regarding the alternative hypothesis, it claims that the model can be used and that at least one slope parameter is not equal to zero. It also states that there will be a statistically significant association between one or more predictor variables. According to statistics, it is as follows: Ha: β1 ≠ 0 or β2 ≠ 0d. The significance level is 0.001 or 1%.
e. Review the table above.
f. The test's conclusion informs us that the alternative hypothesis should be accepted while the null hypothesis should be rejected. The findings show that the factors have a statistically significant association. so that it can be used
It was possible to predict the number of wins during the regular season using at least one predictor variable that was statistically significant. The data for each parameter were used for a t-
test: Score average: 0.2406/0.0043 =5.657. Relative skill average: 0.0348/0.005 = 6.421. The average point difference is 13.298 (1.7621/0.127). 0.876 or 87.6% is the coefficient of determination. A team that scores 75 points per game on average, has a relative skill level of 1350, and has a point differential of -5 is predicted to win 20 games throughout the regular season. A squad with a talent level of 1600, an average scoring output of 100 points per game, and a point difference of +5 is predicted to win 43 games throughout the regular season.
7. The final phase We draw the conclusion from the study's findings that there is a statistically significant association between the team's future success and its past performance. According to the data, teams with a better relative skill level, point differential, and greater average points scored per game have a higher likelihood of winning more frequently. Will win more games throughout the regular season, or to put it more simply. The research, or tests, in this model have a practical value. Upper management and the coaching staff can review the provided data and, where they consider it necessary, modify, tweak, and improve the team's performance in the areas of skill
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level and the average. We can only hope that these adjustments will lead to higher point averages
and point differentials. There will be more triumphs as a result of these modifications.