MAT 243 Project Three Summary Report Template
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School
Southern New Hampshire University *
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Course
243
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
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6
Uploaded by SuperComputerLeopard33
MAT 243 Project Three Summary Report
[Amber Smith]
[amber.smith33@snhu.edu]
Southern New Hampshire University
1.
Introduction
The data set to analyze will be average of points scored, average point differential, the relative skill average, and the total number of wins regarding my team and the opposing teams. The usage of this data will be to look at the measure of achievement and to try to be able to see what areas need to be worked on 2. Data Preparation
“avg_pts_differential” will look at the average point differential between my team and opposing teams. It will allow us to look at the point variation. “avg_elo_n” will measure the average relative skill of the team. The higher the relative skill of a team that team will have the probability of beating a team with lower relative skill. 3. Simple Linear Regression: Scatterplot and Correlation for the Total Number of Wins and Average Relative Skill
Data visualization techniques are used to examine the relationship between data.
If the data is in a pattern where one variable increases while the other variable decreases, this would indicate a negative relationship. If both variables increase that is a positive relationship. If the data has no pattern then there is no relationship. The parameters of coefficient of correlation values are -1 to +1. The correlation coefficient value notifies us of the direction of the relationship between two variables with a positive or negative symbol. The value of the correlation coefficient represents the strength of the affiliation of the two utilized variables. If the value is 0, this would indicate there is no affiliation between
the two variables. -1 would represent a negative relationship between two variables that is absolute. While +1, represents an absolute positive affiliation between two variables
The scatterplot shows the data in an increasing pattern. The Pearson Correlation Coefficient is 0.4777 which is 47.77%, which means the total number of wins increase or decrease as the number of points scored increase or decrease. The scatterplot has a value for p as 0.00
4. Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill
Simple linear regression estimates a relationship between the response and predictor variable. The equation for this is (Y) = βo + β1X1. Bo will represent the total number of wins and B1 will represent the average number of points scored. The results of the overall F- test is as follows: The null hypothesis illustrates the average points scored and is equivalent to zero. The null hypothesis is not significant. It is statistically notated as such: ( β1 = 0 )b. The alternative hypothesis illustrates the average points scored and does not have an equivalence to zero. It has a significant and is as such: (β1 ≠ 0)c. The level of significance is 1%
Table 1: Hypothesis Test for the Overall F-Test
Statistic
Value
Test Statistic
1520.00
P-value
0.00
With the p value being zero we reject the null hypothesis and accept the alternative. 5. Multiple Regression: Scatterplot and Correlation for the Total Number of Wins and Average Points Scored
The scatterplot shows a correlation 0.9072. This relates that there is a strong relationship between relative average skill and total number of wins. The correlation coeffient is strong because the p value is less than 0.001. We reject the null hypothesis due to this.
6. Multiple Regression: Predicting the Total Number of Wins using Average Points Scored and Average Relative Skill
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Hypothesis Test for the Overall F-Test Statistic
Value
Test Statistic
1580.00
P-value
0.00
A multiple linear regression would be used to analyze a response variable with multiple predictors. The equation would be Y = βo + β1X1 + β2X2 + . . -152.5736 + 0.3497 (X1) + 0.1055(X2)
The null hypothesis states that the model is not practical in use. Additionally, all slope parameters are equivalent to zero. The null hypothesis is statistically notated as :Ho: β1 = β2 = 0b. The alternative hypothesis states that at least one parameter is not equivalent to zero. It is statistically notated as such: H2: β1 ≠ 0 c. The level of significance is 0.01 or 1%. With the p-value being zero the null hypothesis would
be rejected. The results based on the total F-Test shows at least one of the predictor variables is statistically significant with the number of wins. We derive from the t-test, the p-value-, which was less than 1%, gives us a conclusion stating that all of the predictors have statistical significance. A t-test, was utilized for the following parameters: point average: 0.3497/0.048 = 7.297. Average relative skill: 0.1055/0.002 = 47.952.The coefficient of determination is equivalent to 0.837 or 83.7%. This signifies that the variance in the totality of wins can be interpreted by the variance concerning relative skill average, and point’s average. 07. Multiple Regression: Predicting the Total Number of Wins using Average Points Scored, Average Relative Skill, Average Points Differential, and Average Relative Skill Differential
Table 3: Hypothesis Test for Overall F-Test
Statistic
Value
Test Statistic
1449
P-value
0.00
The equation for the multiple regression model Y = βo + β1X1 + β2X2 + E
At least one of the predictor variables was statistically significant and could forecast the
number of wins during the regular season. A t-
test was performed utilizing the data for each
parameter: average points scored: 0.2406/0.0043 =5.657. Average relative skill: 0.0348/0.005 = 6.421. Average points differential: 1.7621/0.127
= 13.298. the coefficient of determination shows
0.876 or 87.6%.
At least one of the predictor variables was statistically significant and could forecast the number of wins
during the regular season. A t-test was performed utilizing the data for each parameter: average points scored: 0.2406/0.0043 =5.657. Average relative skill: 0.0348/0.005 = 6.421. Average points differential: 1.7621/0.127 = 13.298. the coefficient of determination shows0.876 or 87.6%.
8. Conclusion
We can conclude after the data that there is a significant relationship between relative skill and wins or losses. From the analysis, we conclude that the teams who possess a higher relative skill level, point differential, and higher points each game average, have a higher probability for victory more often than not. The coaches can make changes to help with higher points and higher relative skill and maybe more victories. 9. Citations
You were not
required to use external resources for this report. If you did not use any resources, you should remove this entire section. However, if you did use any resources to help you with your interpretation, you must
cite them. Use proper APA format for citations.
Insert references here in the following format:
Author's Last Name, First Initial. Middle Initial. (Year of Publication). Title of book: Subtitle of book, edition. Place of Publication: Publisher.
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