Senior Management at Esil University believes that decreases in the number of undergraduate applications that they have experienced are directly related to tuition increases. They have collected the following enrollment and tuition fees data for the past decade:
Year: Undergraduate Applications: Annual Tuition Fees(GBP)
1 6,050 3,600
2 4,060 3,600
3 5,200 4,000
4 4,410 4,400
5 4,380 4,500
6 4,160 5,700
7 3,560 6,000
8 2,970 6,000
9 3,280 7,500
10 3,430 8,000
a)Develop a linear regression model for these data and forecast the number of applications for Esil University if tuition fees increase to 9000 gbp per year and if tuition fees are lowered to 7000 gbp per year.
b)Determine the strength of the linear relationship between undergraduate applications ad tuition fees by using correlation.
c)Describe the various decisions for Esil University that would be affected by the forecast for undergraduate applications.
d)Develop an exponential smoothing model with a=0.20 for these data to forecast undergraduate applications in year 11 and compare its accuracy to the forecast developed in part a).
The regression equation is
apps = 6542 - 0.449 fees
The prediction you want can be found by plugging 9000 in where the word fees is in the equation. However, regression models are not used to predict trends outside of the data range in most cases...just an FYI.
Based on the p values below and the R^2 value we can see that this is not a very good model. Usually the p value should be lower and .05 and R^2 should be above 90 (some people say above ...
The regression equation is clearly utilized.