Question

2) Student Population Data From Western Carolina University

Number	Year	Enrolled
1	2006	8,860
2	2007	9,056
3	2008	9,050
4	2009	9,429
5	2010	9,407
6	2011	9,352
7	2012	9,608
8	2013	10,107
9	2014	10,382
10	2015	10,340
11	2016	10,805
12	2017	11,034
13	2018	11,639

3) What is the correlation between year and student population?

4) What is the regression model for the data? Is this a good model?

5) What do you predict the student population will be in 2019?

Answer 1

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used: х Y X*Y x2 Y2 2006 8860 17773160 4024036 78499600 2007 9056 18175392 4028049 82011136 2008 9050 18172400 4032064 81902500 2009 9429 18942861 4036081 88906041 2010 9407 18908070 4040100 88491649 2011 9352 18806872 4044121 87459904 2012 9608 19331296 4048144 92313664 2013 10107 20345391 4052169 102151449 2014 10382 20909348 4056196 107785924 2015 10340 20835100 4060225 106915600 2016 10805 21782880 4064256 116748025 2017 11034 22255578 4068289 121749156 2018 11639 23487502 4072324 135466321 Sum = 26156 129069 259725850 52626054 129040096 9

Based on the above table, the following is calculated: 72 X X; 26156 13 - 2012 n n Y =įy; = 129069 13 9928.3846153846 n 2 72 72 1 SSxx X; 52626054 - 261562/13 = 182 n i=1 i=1 2 72 1 SSyy = Y; ΣΥ; = 1290400969 – 1290692/13 = 8954295.0769229 n i=1 i=1 12 72 1 SSxy = x; Y; ΣΧΥ - ΣΧ; x) Yi 259725850 - 26156 x 129069/13 = 39022 n Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows: m = SSXY 39022 214.4066 SSxx 182 n =Y – X… m = 9928.3846153846 – 2012 x 214.4066 = -421457.6813 Therefore, we find that the regression equation is: Y = -421457.6813 +214.4066X

Therefore, based on this information, the sample correlation coefficient is computed as follows r= SSXY SSXX SSyy 39022 V182 x 8954295.077 = 0.967

Since, the correlation coefficient is close to 1 , we can say that the model is good.

For X = 2019