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CA_GPS_6 - 1 Construct a scatter plot of the data in the...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 6 1.6 FITTING LINES TO DATA POINTS: MODELING LINEAR FUNCTIONS Class Time: ____________ Date: __________ Useful Definitions: * Linear Model : A linear model is an equation of the form bx a x f + = ) ( , * Linear Regression (the least-square method): A procedure which defines the best-fit line as the line for which the sum of the squares of vertical distances from the data points to the line is a minimum. * Constant first differences : If the first differences of data outputs are constant (for equally spaced inputs), a linear model can be found that fits the data exactly. If the first differences are “nearly constant,” a linear model can be found by an approximate fit for the data. * Discrete : It is used to describe the data or a function that is presented in the form of a table or in a scatterplot. * Continuous : It is used to describe a function or graph when the inputs can be any real number.
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Unformatted text preview: 1. Construct a scatter plot of the data in the table. Can the scatter plot be fit exactly or only approximately by a linear function? How do you know? Find the linear function that is the best fit for the data. x 2 6 10 14 18 y 2 4 6 8 10 2. a) Find the least-squares regression line in the form bx a x f + = ) ( . b) Use the regression line to estimate y when 150 = x (interpolation) and 200 = x (extrapolation). x 100 120 140 160 180 y 477 483 489 495 504 3. If $400 is invested at 4% simple interest, the future value S in t years is given in the table below. a) Is the rate of change of the future value constant for uniform inputs? b) Can the future value be modeled by a linear function? c) Write the equation that gives the future value as a function of the time in years in slope-intercept form. Year(t) 0 1 2 3 4 Future Value (S) 400 425 450 475 500...
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