## Question 765:

1

1. Q765_1_regressionQ765.xls

The analysis is shown below and the calculations are available in the attached excel file.

Part a

First we run the correlations between each variable. The correlation matrix is shown below with the p-values for each correlation. These can be obtained by entering the pairs of values in the X and Y columns in the spreadsheet.

Year  Season-Ticke    % games won

Season Ticke         0.974

0.000

% games won         -0.030         0.015

0.939         0.969

No. Active A         0.979         0.956        -0.263

0.021         0.044         0.737

We see strong and statistically significant correlations between season ticket sales and year r = .974 (p < .0001), as well as between the Number of active alumni r = .979 (p < .05) and between Number of active alumni and season ticket sales r = .956 (p < .05).  We interpret these relationships as the year increases (more recent years) there are more season ticket sales. As the number of active alumni increase, so to do the number of season ticket sales.

There is a slight negative correlation between % of games won and Number of active alumni, however the relationship is not significant p > .73.  The magnitude of this correlation is modest (r = -.263) and perhaps with a larger sample of years it will be significant (since there were only 4 data points to correlate b/c there are only data for 4 years of active alumni).  The correlations between % of games won and year and between % of games won and season tickets are not significant and the magnitude of the correlation (near 0) suggest there is no relationship between these variables.

Part b

Season Ticket Sales = 10528 + 3.5 (% games won)

The y-intercept is 10528 (where the line crosses the y-axis) and the slope of the regression line is 3.5. We see that season ticket sales are positively correlated with the percent of games won. There is a positive correlation between these two variables. The relationship would not be considered statistically significant since the p-value is above .9.

Part c

Season Ticket Sales = 5834 + 1.06 (No. Active Alumni )

The y-intercept is 5834 (where the line crosses the y-axis) and the slope of the regression line is 1.06. We see that season ticket sales are positively correlated with the number of active alumni, that is, there is a positive correlation between these two variables. The relationship IS statistically significant since the p-value is below .05.