Project 3 Final.docx

MAT 243 Project Three Summary Report Southern New Hampshire University

1. Introduction In looking at this dataset, we are looking at simple linear regression and multiple linear regression. The problems we’re going to look at throughout this paper are total number of wins and average relative skill, predicting total wins based on relative skill, total wins and average points scored, predicting total wins from average points scored and relative skill, and total wins based on average points scored, relative skill, average point differentials, and relative skill differentials. The results will be used to predict the total wins that can be expected during the regular season based off the current relative skill of the team. We will look at how relative skill can affect the predicted total of wins as well as how average points earned per game affects the probability of winning games. The type of analysis I’ll be using for this project is inferential statistics, which is where we draw conclusions from the data that we have. In this case we have average points, average relative skill, average point differential, average skill differential, and total wins. 2. Data Preparation The variable avg_pts_differential represents the difference between the points scored by a team and their opponents. This can be explained to someone easily by stating the team has won a game 30 – 20 which means our point differential would be 10, as the team plays more and more games you add all the teams points together by all their opponents and then divided by the number of games that have been played. The variable avg_elo_n represents the average relative skill of each team. You can explain this to someone by letting them know it is calculated based on the final score of the game, the game location, and the probability of the outcome. If a game is won by a team by 10 points on their

home field, we can look at the previous games that were played at their home field and look at how many wins to losses they have and average it out to say they have X% probability to win at home games. 3. Simple Linear Regression: Scatterplot and Correlation for the Total Number of Wins and Average Relative Skill The visualization technique is used to study the relationship trends between two variables with a contingency table. A contingency table consists of rows, column totals, and the total count of the study/observation. The Pearson correlation coefficient is used to measure the strength and direction of a linear relationship between two variables. The range of the correlation coefficient value is -1 to +1. The sign of the correlation value tells us about the direction of the association between two variables, the value of the correlation tells us about the strength in the association. Since our coefficient is 0.9072 that is 90.72% which would be a strong correlation.

The scatterplot and Pearson correlation coefficient tell us the total number of wins and average relative skill. Since the data is in increasing order, this indicates that as average relative skill increases the total number of wins also increases. This is a positive relation between the two variables. Since the coefficient is 90.72% this tells us that as relative skill increases the team has a 90.72% chance to win. The Pearson correlation coefficient is 0.9072, that’s 90.72% which tells us as average relative skill increases or decreases the total number of wins would increase or decrease. The p-value is 0.0. Since the p-value is 0.0 which is less than 0.01 yes, the correlation coefficient is significant. 4. Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill The simple linear regression model is used to predict the total number of wins using average relative skill.

The regression equation is y = -128.475 + (0.1121 * x). H0: All the coefficients are equal to 0 or are not significant. H0: B1 = 0 HA: At least one of the coefficients is significant. HA: B1 ≠ 0 Level of significance is 0.05. F-statistic = 2865 and the p-value is 8.06e-234. Table 1: Hypothesis Test for the Overall F-Test Statistic Value Test Statistic 2865.00 P-value 8.06e-234 Yes, we can conclude that the total number of wins in the regular season can be predicted by average relative skill, because the p-value is less than the level of significance. Predicted total number of wins in a regular season with relative skill of 1550: Y = -128.475 + (0.1121 *X) Y = -128.2475 + (0.1121 * 1550) = 45.5075 Y = 46 wins with a relative skill of 1550. Predicted total number of wins in a regular season with relative skill of 1450:

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help