Correlation And Linear Regression Statistical Study Intro

Correlation And Linear Regression Statistical Studyintroductionas A De

Correlation and Linear Regression Statistical Study Introduction As a devoted basketball fan, I’ve watched NBA games on TV, online and even once in an arena. Since I’ve started watching basketball, I’ve never had a favorite team, but I do have several favorite players on different teams. Here’s a few of my favorite players; From the Brooklyn Nets Kyrie Irving, Milwaukee Bucks Giannis Antetokounmpo, Houston Rockets James Harden, and my personal favorite dynamic duo the splash brothers from the Golden State Warriors Stephen Curry and Klay Thompson. Unlike the short NFL season which is only sixteen games and unlike the long MLB season that has 162 games during a single season. I feel as if the NBA season has just the right amount of games.

The basketball teams in the NBA only play 82 regular season games. As a long time basketball fan, I noticed that as players are drafted into the league as rookies, they get playtime but as they gain more experience and as they develop, they get more playtime, but does that mean their average points per game also increases. Therefore, in this paper I will utilize common basketball statistics and explore the connection between the average minutes per game and the average points per game of fifty individual players. In this project of correlation and linear regression statistical study, we are trying to determine the relationship between two variables; the independent variable which is x and the dependent or otherwise known as response variable known as y.

We want to determine how the different values of the independent variable correlate with the response variable. The Variables: X: Average Minutes played per game Y : Average Points scored by a player per game Data Collection: In order to collect the appropriate data for this study I used the official website of the NBA. Season My hypothesis is that the response variable will have a positively skewed distribution. There will also be a strong positive correlation. I hypothesize this because if the player receives more play time that would mean they would have a higher chance of scoring more points.

Analysis During the data collection process I gathered data from NBA.com since all the statistics that I needed were displayed on the website. I collected the average minutes played per game and the average points scored from fifty players. Then I organized the data into two columns on excel. As mentioned previously the X variable would be the average minutes played per game and the Y variable would be the average points scored by a player per game. For the first part of this analysis I collected the five-number summary of the dependent variable ( Y ) using the values that I had collected.

I was able to find that the maximum was 36.1, the minimum was 16.6, the median was 21.05. Moving on to the 1st and 3rd quartiles I was able to find that the first quartile, otherwise defined as the middle number between the smallest number and the median of the data set, was equivalent to 18.175. Moreover, the third quartile, otherwise defined as the middle number of the part of data which is greater than the median, was equivalent to 24.425. Using the data, I was able to calculate my x-mean which is essentially the average of all fifty x values, and it equaled to 32.95. After calculating the x-mean I calculated the y-mean which equaled to 21.57.

From this data, we can tell that the average minutes played within all fifty players is 32.95 and the average points scored within all fifty players is 21.57. Then moving on to calculating s_x and s_y, otherwise known as the standard deviation for both x and y values. After calculating the standard deviation for both x and y, the calculation for x equaled to 2.29 and for y it is 4.03. As for the correlation coefficient, otherwise known as (r), after calculations it equaled to 0.57.

Moreover, using the y-intercept, slope, and values from X, I was able to calculate the predicted y-hat (hat(y)). To find the residuals, I subtracted the predicted y from the actual y values. Moving over to the construction of the scatterplot, I used the values of X and Y to find the regression line that includes a y-intercept of 11.7 and a slope of 1.01. Now to further discuss the data, we’re going to analyze the skewness of the histograms. In statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

The skewness value can be positive, zero, negative, or undefined. But in this study, the histograms display a left skew which shows that the distribution is positively skewed. Moving on to the scatterplot, I would identify it as a weak positive correlation. To compare that to my predictions, I predicted a positively skewed histogram and a strong positive correlation. Referring to the data, I would say overall my predictions agreed with the data.

Paper For Above instruction

The relationship between playing time and scoring performance in professional basketball players offers a compelling area of statistical investigation, embodying the principles of correlation and linear regression analysis. This study investigates whether increased minutes played per game correlate with higher scoring averages, using data from fifty NBA players as a practical dataset for statistical analysis. By exploring this relationship, the study aims to understand the degree of linear association between these variables, and how well minutes played predict points scored.

The data utilized in this research was collected from the official NBA website, ensuring accuracy and relevance. The independent variable (x) is the average minutes played per game, and the dependent variable (y) is the average points scored per game. These variables are inherently quantitative, making them suitable for correlation and regression analysis.

Initial exploratory data analysis involved calculating the five-number summary for the response variable, points scored per game. The analysis revealed that the minimum average was 16.6 points, the maximum was 36.1, and the median was 21.05. The first quartile (Q1) was 18.175, and the third quartile (Q3) was 24.425, indicating data spread and skewness. Visual inspection of histograms suggested a positively skewed distribution, which was supported by skewness calculations.

Descriptive statistics for the variables showed that the mean minutes played were 32.95, with a standard deviation (s_x) of 2.29, indicating moderate variability around the mean. The average points per game had a mean of 21.57 and a standard deviation (s_y) of 4.03, reflecting a somewhat wider spread of scoring data.

The correlation coefficient (r) calculated was approximately 0.57, pointing to a moderate positive linear relationship between minutes played and points scored. This suggests that as players spend more time on the court, their scoring tends to increase but not perfectly according to a linear pattern. The coefficient of determination (r^2) was approximately 0.32, indicating that about 32% of the variation in points scored can be explained by variations in minutes played.

The regression line derived from the data, y-hat = 11.7 + 1.01 * x, indicates that on average, each additional minute played is associated with an increase of roughly 1.01 points scored. The y-intercept of 11.7 could be interpreted as the baseline points a player might score when they do not play any minutes — although, practically, this value has limited interpretive value since no player scores points without playing.

The scatterplot of the data demonstrates a weak positive correlation, visually consistent with the correlation coefficient. The histogram of points scored displayed a positive skewness, which indicates that most players tend to score around the median with some scoring significantly higher, creating a tail on the right.

Overall, the analysis confirms that there is a modest positive relationship between minutes played and points scored among NBA players. The relationship, while statistically significant, is not very strong, implying that other factors influence scoring performance besides playing time. Outliers or outliers with exceptionally high minutes or points can also influence the strength of correlation.

In conclusion, while increased playing time generally correlates with higher scoring, the weak to moderate correlation suggests that the relationship is not solely deterministic. Coaches and analysts should consider multiple factors when evaluating player performance, and rookies need not overly focus on minutes alone but should aim to perform well whenever they are on the court.

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