The data suggests that the distribution of percentage Alumni donation rate is normally distributed with estimated mean of 29 and standard deviation of 13.44. Scatter plot of Alumni giving rate and Graduation rate. The plot suggests a statistically significant [F(1,46) = 61.3, P < .001) positive correlation of .756 between graduation rate and alumni donation rate.
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The higher the graduation rate, the higher the alumni donation rate. The alumni donation rate ranged from 7% (University of California – Davis of CA) to 67% (Princeton University of NJ) with a mean of 29.3% (SD 13.4) whereas graduation rate ranged from 66% (University of Texas – Austin of TX) to 97% (Harvard University of MA) with a mean of 83% (SD 8.6). The regression equations giving the average relationship between the variables are: Alumni donation rate: -68.8 + 1.2 times graduation rate. I.e. Donation rate increases 1.2% on an average for every 1% increase in graduation rate. Variation in graduation rate could explain 57% variation in Alumni giving rate. Scatter plot of Alumni giving rate and percentage of classes under 20 The percentage of classes under 20 ranged from 29 (U. of Illinois-Urbana Champaign of IL) to 77 (Yale University of CT) with a mean of 55.7 (SD13.2). There is positive correlation (r = .646, F(1,46) = 32.9, P < .001) between the variables and the average relationship is expressed as: Alumni giving rate (%) = -7.4 + 0.66 times percentage of classes under 20. i.e. every 1% increase in percentage of classes under 20 increase the Alumni donation rate by 0.66%, on an average. Variation in percentages of classes under 20 explains 41.7% variation in Alumni donation rate. Relationship between Alumni donation rate and student/faculty ratio The Student/Faculty ratio ranged from 3 (California Institute of Technology of CA) to 23 (University of Florida of FL) with an average of 11.5 (SD 4.9). The observed correlation coefficient of -.742 does suggests a negative association between the variables at the population level [F(1,46) = 56.5, P < .001). Mathematical expression modeling the average relationship between the variables is: Alumni donation rate = 53 – 2.1 times Student/faculty ratio. Every unit increase in the student/faculty ratio brings down the alumni donation by 2.1%, on an average. Variation in student/faculty ratio could explain 55.1% variation is Alumni donation rate. Distribution of Alumni giving rate (%) in colleges from the East and the West The difference in the mean of percentage of Alumni donation rate in colleges from the East (n= 25,
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