Using the data2 below, we are going to forecast the number of Science and Engine
ID: 3149623 • Letter: U
Question
Using the data2 below, we are going to forecast the number of Science and Engineering degrees to be awarded per 1,000 individuals ages 18-24 years old in Arizona in 2019.
Table 2: Bachelor's degrees in science and engineering conferred per 1,000 individuals 18-24 years old, by AZ: 1990-2011
a) Determine what type of mathematical model may best t the year vs. science & engineering bachelor's degrees data, by calculating the coecient of determination. Choose from linear, quadratic, cubic, exponential, or logarithmic. Explain why you think the function you chose is the best choice, then use regression to find the function D(y).
b) Determine what type of mathematical model may best t the year vs. population data, by calculating the coecient of determination. Choose from linear, quadratic, cubic, exponential, or logarithmic. Explain why you think the function you chose is the best choice, then use regression to nd the function P(y).
c) Use the results in (a) and (b) to nd the number of of Science and Engineering degrees to be awarded per 1,000 individuals ages 18-24 years old in Arizona in 2019.
Year Science & Eng. Bachelor's Degrees Population Degrees per 1,000 individuals 1990 3, 730 395, 969 9.4 1991 3, 926 388, 245 10.1 1992 4, 191 389, 767 10.8 1993 4, 410 395, 208 11.2 1994 4, 395 406, 442 10.8 1995 4, 700 413, 693 11.4 1996 4, 878 417, 142 11.7 1997 5, 037 430, 444 11.7 1998 5, 310 444, 734 11.9 1999 5, 154 519, 627 9.9 2001 5, 159 536, 018 9.6 2002 5, 914 549, 407 10.8 2003 6, 386 559, 859 11.4 2004 7, 268 571, 196 12.7 2005 7, 741 580, 341 13.3 2006 8, 174 591, 986 13.8 2007 8, 917 605, 860 14.7 2008 9, 503 621, 451 15.3 2009 10, 173 629, 438 16.2 2010 11, 183 634, 855 18.7 2011 13, 812 643, 726 21.5Explanation / Answer
a) Linear Regression equation is given by
The regression equation is
Degrees = - 752914 + 380 year
R-Sq = 85.1%
The quadratic regression equation is
Degrees = 1.02E+08 - 102178 year + 25.63 year**2
R-Sq = 96.8%
The regression equation is
Degrees = - 1.45E+10 + 21869267 year - 10957 year**2 + 1.830 year**3
R-Sq = 98.7%
We can do regression fit using the following path in minitab
Stat-Regression-Regression
For nonlinear regression use the following path
Stat-regression-Fitted Line plot
R square is the coefficient of determination it shows the percentage of variation explained by our predicted model.
Here In cubic case not much improvement has happened than from quadratic regression so for
simplicity of the model we choose the quadratic model as best fit.
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