Thursday, November 25, 2010

Ch. 1 - Modeling with Functions and Regression Equations

Chapter 1 talks about different types of functions and how each function look like when we graph them. For this project, we will be focusing on the 2 most common functions (or equations) that we see over and over again throughout the courses of math: linear and quadratic equations. Linear function can be represent by f(x)=x and can be written as Ax+B in equation form from our previous chapter. Meanwhile, a quadratic function is represented as f(x)= x2 and can be written as Ax2+Bx+C.

In this project, we're trying to graph the given data with the most accurate function as possible. The line on the graph that model the most relative to the given data is called the regression line. But in order to find the regression line, we need to consider the correlation coefficient "r" and coefficient of determination "R
2", where R2 is needed to predict the future outcome base on the relative data. However in this case, both r and R2 will be the correlation coefficient where the closer the number gets to 1, the better the curve fits the data.
  • First of all, we need to input the data (years) into the table of the graphing calculators. To do that, hit STAT > EDIT > ENTER. A table will appear with the headings L1, L2, etc. For this problem, L1 will be the input x-values in years. And L2 will be the output y-values in average hour earnings.
  • After you have entering all the data, you're ready to find the regression equations. In order to find the regression equation (for now we just need to find the linear and quadratic regression equations), we hit STAT > CALC > 8:LinReg(a+bx) > ENTER to find the linear regression equation.
  • After the linear regression appear, hit 2ND > 1 (for L1), 2 (for L2), > VARS > Y-VARS > 1:Function > ENTER > 1:Y1 > ENTER. If you follow the steps correctly, you should be able to get the first picture. Press ENTER again to get the second picture where you will see the equation of linear regression and the correlation coefficient "r". (The equation also appear in Y1 if you go to Y= )
  • The same procedures apply for finding quadratic regression equation. Only instead of choosing 8:LinReg, you hit STAT > CALC > 5:QuadReg > ENTER. Continue following the rest of the steps from linear regression and you should be able to get something like the pictures below.

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