1) What is the quality measure we use to check the validity of the model? 2) Whi

Question

1) What is the quality measure we use to check the validity of the model?

2) Which of the following is the correct interpretation of the "graduation rate" coefficient?

3) How do you interpret the value of the intercept b0?

4) As student/faculty ratio increases, how does this affect giving rate and why?

5) Based on a t-test and 5% level of significance, we can conclude that the coefficient of the following independent variable(s) is 0:

6) What does the coefficient of determination for this regression implies?

Alumni donations are an important source of revenue for universities. One fundraiser is trying to create a model to predict alumni giving rate as a function of 1) graduation rate, 2) percentage of smaller class sizes and 3) student/faculty ratio. The hypothesized model is: In this equation, y is alumni giving percentage (i.e. 20), xi is graduation percentage (i.e. 80), x2 is percentage of classes with less than 20 students (i.e. 50), and x is student/faculty ratio A regression analysis of 48 national universities resulted in the following output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.836624531 0.699940606 0.679482011 7.609724781 48 oand Font Styles Editing Regression Residual Total 5943.531072 1981.177 34.21255 .43233E-11 44 2547.948094 57.9079 47 8491.479167 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% 20.7201343 17.52136501 1.18256 0.243333 -56.03212475 14.5918561 0.748182799 0.165959959 4.508213 4.8E-05 0.413712483 1.08265312 % of Classes Under 20 0.029040648 0.139321322 02084440.835844-0251743023 0.30982432 Student Faculty Ratio .19201069 0.386723104 -3.08234 0.003538 -1.971399888 -0.4126215 Intercept Graduation Rate

Explanation / Answer

1)      We use R square to check the validity of the model. Low r square implies the model does not fit data well. High R square implies the model fits the data well.

2)      The graduation rate coefficient = 0.748182799 is interpreted as for every one unit increase in the graduation percentage the average value of alumni giving rate will increase by 0.748182799 while % of classes Under 20 and Student/faculty ratio remains constant.

3)      The intercept b0 = -20.7201343 is interpreted as we would expect average value of alumni giving rate is -20.7201343 if graduation rate, % of classes Under 20 and Student/faculty ratio are zero.

4)      As student/faculty ratio increase the average value of alumni giving rate will decrease by 1.19201069 because coeffcient of student/faculty ratio is negative.

5)      As the p value of coefficients of % of classes Under 20 and Student/faculty ratio are greater than 0.05. So we failed to reject null hypothesis. We conclude that coeffcient of the independent variable % of classes Under 20 and Student/faculty ratio are zero. While P value for coefficients Graduation rate variable are less than 0.05 so we can conclude that coeffcient of the independent variable Graduation rate is not 0.

6)      The Coefficient of Determination: It tells you how many points fall on the regression line. 70% means that around 70% of the variation of y-values around the mean are explained by the x-values. In other words, 70% of the values fit the model.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.