Question

. The chancellor of a small regional college is concerned about the declining freshmen enrollment at his college. A number of the decline, but the chancellor believes it is directly related to annual tuition increases. He has collected the following data for the past 8 years Year Freshman enrollment Annual tuition (in U.S. Dollars) 6550 6230 5980 5540 4960 4630 4220 32000 37000 45200 45700 46200 46700 5200 57700 a. Develop a linear regression equation for forecasting freshman enrollment as a function of the annual tuition. b. Forecast freshman enrollment if the annual tuition increases to US$9,000 in year 9. c. Evaluate the "goodness of fit of the regression equation by computing the values of R,r, and s, and interpret the results

Answer 1

the regression analysis is given above in excel figure.

Freshman Annual 1 Year enrollment tuition 6550 32000 6230 37000 5980 45200 5540 45700 496046200 4630 46700 4520 52200 422057700 3 2 6 5 SUMMARY OUTPUT Regression Statistics 10 Multiple PR R Square Adjusted R Square Standard Error Observations 0.909612846 0.827395529 0.798628117 389.7363876 12 13 15 16 17 18 19 ANOVA MS icance F Regression Residual Total 1 4368720.789 4368720.789 28.76155605 0.001723234 6 911366.7108 151894.4518 5280087.5 21 Coefficients Standard Error t Stat p-value Lower 95% Upper 95 % Lower 95.0% Upper 95 .0% 23 Intercept Annual tuition 9795.48779 844.2048133 11.60321244 2.46662E-05 7729.793031 11861.18255 7729.793031 11861.18255 0.098521925 0.0183707425.362980146 0.001723234-0.143473512-0.053570339 -0.143473512 -0.053570339 25

regression equaltion: y = -0.0985x + 9795.49

y = freshman enrolled

x = tuition fees

If the fees is increased by 9000

new fees = 57700 + 9000 = 66700

Hence x = 66700

Freshman enrollment = -0.0985*66700 + 9795.49 = 3225.54 = 3226

c) R = 0.9096

R squared = 0.8273

Standard error S = 389.736

The R and R squared tells us that the 82% of the data is proportional of explains the obtained result. Which is a good number. But the S of 389 says that there is potential for a huge error in this result. Hence, more observations would help us reduce the error in the analysis.