document.write( "Question 1183372: Each ordered pair (t, N) represents the year t and the number N (in thousands) of female participants in high school athletic programs during 13 school years, with t = 1 corresponding to the 2000 - 2001 school year.
\n" ); document.write( "(1, 2783), (2, 2809), (3, 2852), (4, 2865), (5, 2907), (6, 2954), (7, 3020)(8,3055), (9, 3111), (10, 3172), (11, 3175), (12, 3225), (13, 3235)
\n" ); document.write( "Use the regression feature in your graphing calculator to find the following models and their coefficient of determination. Round to 4 decimal places.
\n" ); document.write( "a.Linear Model:𝑁(𝑡)=2723.5385+41.2857t
\n" ); document.write( "𝑟2=0.9873
\n" ); document.write( "Exponential Model:𝑁(𝑡)= (2732.9970)(1.0138)^t
\n" ); document.write( "𝑟2= 0.9874
\n" ); document.write( "Power Model:𝑁(𝑡)= 2685.2908t^0.0655
\n" ); document.write( "𝑟2= 0.8696
\n" ); document.write( "(d)Which model best fits the data? Explain.\r
\n" ); document.write( "\n" ); document.write( "(e)Use the model you chose in part (d) to predict the school year in which about 3,727,000 girls will participate. \n" ); document.write( "

Algebra.Com's Answer #813657 by ikleyn(52878) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Hello, in this post, I see three regression models, written without explanations about their origins.\r\n" );
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document.write( "OK, I will suppose that you (or somebody else) produced these models, and I will not check if they are correct.\r\n" );
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document.write( "Question (d) asks which model is better.\r\n" );
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document.write( "Near to each model, I see the parameter r^2 (with no explanations on its meaning).\r\n" );
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document.write( "Usually, in such problems, r^2 denotes the calculated sum of quadratic point-to-point deviations of the points from the regression.\r\n" );
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document.write( "If so, then the best regression is where r^2 is minimal.\r\n" );
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document.write( "So, the Power Model looks like the best.\r\n" );
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document.write( "Regarding part (e), write this equation for the Power Model\r\n" );
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document.write( "    2685.2908t^0.0655 = 3727,\r\n" );
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document.write( "take logarithm base 10 of both sides\r\n" );
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document.write( "    log(2685) + 0.0655*log(t) = log(3727)\r\n" );
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document.write( "express and calculate log(t)\r\n" );
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document.write( "    log(t) =  = 2.17\r\n" );
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document.write( "and restore t\r\n" );
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document.write( "    t =  = 148 years.\r\n" );
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document.write( "So, the prediction is 148 years after 2000.\r\n" );
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document.write( "Honestly, this result seems to be strange to me, but i got it formally from your data.\r\n" );
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document.write( "I have serious suspitions, that either the problem is defective, or your data related to the regression is incorrect.\r\n" );
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document.write( "But it is just the material for you to search for the truth.\r\n" );
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