Term Paper: NBA Stats

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SAMPLE EXCERPT:

[. . .] 1 (for points). Mean height is 78.7 and mean points is 16.843, so calculating the covariance of this data pair would look like this:

(72 -- 78.7)(13.1-16.843) = 25.0781

In order to develop the value for each pair, two new columns were created in the Excel sheet to calculate the difference of the data point and the mean with the following formulas:

=a2-78.7 (for height, pasted into the other 99 rows which automatically adjust the cell value for each row, as =a3-78.7, a4-78.7, etc.), and =b2-16.843 (for points, also pasted).

A third column with the following formula created the product of each row in these two columns:

=c2*d2 (pasted for all rows).

The average function was used to determine the mean of this last row, which is the covariance: 2.1679. Standard deviations are 3.60274867 (for height) and 3.74805687 (for points), meaning Pearson's coefficient is calculated as:

2.1679/(3.60274867 * 3.74805687) = 0.160545859.

Linear regression attempts to find the line of best fit for a data sample. The basic equation of any line for variables x and y is given as y = a + bx. For a linear regression slope (b) is calculated as:

((n*?xy)-(?x)(?y)) / ((n*?x2)-(?x) 2)

Adding another column to the spreadsheet enabled the quick calculation of height * points (xy) for each data pair, and a column for x2 was also added; the SUM function was used to calculate ?xy (132771.2), ?x (7870), ?y (1684.3), and ?x2 (620654). With n (population size) 100, the slope (b) of the equation becomes:

((100*132771.2)-(7870)(1684.3))/((100*620654)-(78702) = 0.168708171.

The intercept (a) is calculated as:

(?y-b (?x))/n which with the substituted values becomes

(1684.3-(0.168708171*7870))/100 = 3.56566694.

The full linear regression equation for this data set, then, is given as:

points = 3.56566694 + (0.168708171*height)

Chi-square analysis cannot be applied…

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https://www.essaytown.com/subjects/paper/nba-stats-mean-determined/2024569.