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Forecasting

The admission data for freshmen at Tech during the past 10 years is as follows.

Year Applicants Offers % Offers Acceptances % Acceptances

1 13,876 11,200 80.7 4,112 36.7
2 14,993 11,622 77.8 4,354 37.3
3 14,842 11,579 78 4,755 41.1
4 16,285 13,207 81.1 5,068 38
5 16,922 11,382 73.2 4,532 39.8
6 16,109 11,937 74.1 4,655 39
7 15,883 11,616 73.1 4,659 40.1
8 18,407 11,539 62.7 4,620 40
9 18,838 13,138 69.7 5,054 38.5
10 17,756 11,952 67.3 4,822 40.3

Tech's admission objective is a class of 5,000 entering freshmen and it wants to forecast the percentage of offers it will likely have to make in order to achieve this objective.

A. Develop a linear trend line to forecast next year's applicants and percentage of acceptances and use these results to estimate the percentage of offers that Tech should expect to make.

B. develop a linear trend line to forecast the percentage of offers that Tech should expect to make and compare this result with the result in (a). Which forecast do you think is more accurate?

C. Assume Tech receives 18,300 applicants in year 11. How many offers do you think it should make to get 5,000 acceptances?

Solution Preview

A. Develop a linear trend line to forecast next year's applicants and percentage of acceptances and use these results to estimate the percentage of offers that Tech should expect to make.

I made scatterplots, graphing applicants against year, and graphing % acceptances against year. I determined the regression line for these data by going to chart --> add trendline --> linear, and choosing the option to show the line on the chart.
The regression line to predict applicants is applicants = 470.55(year) + 13803, and the ...

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