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5-7: Predict with Linear Models

5-7: Predict with Linear Models. Objectives: Use lines of best fit to make predictions Use linear regression to get the best fitting line Find the zeros of a function Common Core Standards: A-CED-2, F-IF-4, F-BF-1, F-LE-2, G-GPE-5, N-Q-2, S-ID-6, S-ID-7 Assessments:

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5-7: Predict with Linear Models

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  1. 5-7: Predict with Linear Models Objectives: Use lines of best fit to make predictions Use linear regression to get the best fitting line Find the zeros of a function Common Core Standards: A-CED-2, F-IF-4, F-BF-1, F-LE-2, G-GPE-5, N-Q-2, S-ID-6, S-ID-7 Assessments: Define all vocab from this section Do worksheet 5-7 Vocab Quiz Tomorrow!

  2. The line that most closely follows a trend in data is called the Best-Fitting Line. • The process used to find the best-fitting line is called linear regression. • Using a line or its equation to approximate a value BETWEEN two known values is called Linear Interpolation • Using a line or its equation to approximate a value OUTSIDE the range of known values is called Linear Extrapolation

  3. Linear Regression • The calculator can do linear regression for us. • There are specific steps that need to be taken to make sure we do this properly. • On the ti-84 • CATALOG (2nd, 0) • DiagnosticOn • Enter • Enter

  4. Correlation Coefficient • A number between -1 and 1 represented by r that measures how well a line represents a set of data points. • If r is close to 1 it is a close relation with a positive correlation • If r is close to -1 it is a close relation with a negative correlation. • If r is close to 0 it the points are not close to the line.

  5. Turn on Correlation Coefficients • Hit 2nd CATALOG (this is over the 0 button). Go down to DiagnosticOn, hit ENTER then ENTER again. • The closer that the correlation coefficient is to 1 or -1 the better fit the line is.

  6. Least Squares Regression Line • Least-Square regression line- the one and only line for which the sum of the squares of the residuals is as small as possible. • Stat, Edit • L1 are the x values and L2 are the y values • Stat, calc, LinReg(ax+b), Enter *To get the equation to go into y1=, you need to enter- LinReg(ax+b) L1, L2, Y1 y1 is in vars, y-vars, Function, #1

  7. b. Find an equation that models the number of CD singles shipped (in millions) as a function of the number of years since 1993. Approximate the number of CD singles shipped in 1994. c. The table shows the total number of CD single shipped (in millions) by manufacturers for several years during the period 1993–1997. a. Make a scatter plot of the data.

  8. a. Use the equation from the last problem to approximate the number of CD singles shipped in 1998 and in 2000. • In 1998 there were actually 56 million CD singles shipped. In 2000 there were actually 34 million CD singles shipped. Describe the accuracy of the extrapolations made in part (a). • The farther out you get from your actual data the less confidence you have in the accuracy of the number. b. Look back at the last example.

  9. Find the Zeros of a function • Is an x value for which f(x)=0 or y=0. Because y=0 is along the x axis of the coordinate plane, a zero of a function is the x-intercept. • To find a zero set the function = to 0 • 2x-4 • 2x-4=0 • 2x=4 • X=2, 2 is the zero of the function

  10. SOFTBALL Look back at Example 3. Find the zero of the function. Explain what the zero means in this situation.

  11. Using the Calculator to find zeros JET BOATS The number y(in thousands) of jet boats purchased in the U.S. can be modeled by the function y = –1.23x + 14 where xis the number of years since 1995. Find the zero of the function. Explain what the zero means in this situation. Enter the equation into y= Press Graph 2nd Trace 2: Zero Left Bound (an x value left of the zero) Right Bound( an x value right of the zero) Guess (get close to the zero) X=???

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