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Bell Ringer Find each slope: 1. (5, –1), (0, –3) 2. (8, 5), (–8, 7) 1.4 Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions. A line of best fit may also be referred to as a trend line. FOURCurve KINDSFitting OF CORRELATIONS WILL with Linear (YOU Models 1-4 LEARN ABOUT IN TRANSITION) Positive Correlation Constant Correlation Holt McDougal Algebra 2 Negative Correlation No Correlation 1-4 Curve Fitting with Linear Models Scatter Plots + Calculator • 1) STAT • #1 • L1 (x) , L2 (y) (enter data; use arrow keys to select column) • STAT • CALC • 4enter LinReg(ax+b) • 2nd Holt McDougal Algebra 2 • • • • • • • 8) y= plot1 on TYPE X list L1 & Y list L2 mark (select on) GRAPH Example 1 Albany and Sydney are about the same distance from the equator. (a)Make a scatter plot with Albany’s temperature as the independent variable. (b)Name the type of correlation. (c)Then sketch a line of best fit and (d)find its equation. How to: Calculator data entry Enter ______ in list L1 by pressing STAT and then 1. Enter _______ in list L2 by pressing Make scatter plot in the following way: Press 2nd Y= PLOT 1 set up desired type when done, press GRAPH c o n t i n u e d That’s to much work with paper & pencil Tables: ACT Does yours look like this ? example 1 continued Albany and Sydney are about the same distance from the equator. (a)Make a scatter plot with Albany’s temperature as the independent variable. (b)Name the type of correlation. ••• • • • •• •• • (c)Then sketch a line of best fit and (d)find its equation. (hint: what is m? b?) o Example 2 (a)Make a scatter plot for this set of data. (b)Identify the correlation (c)sketch a line of best fit (d)find its equation. example 2 continued Step 1 Plot the data points. Step 2 Identify the correlation. Notice that the data set is positively correlated–as time increases, more points are scored • • • • • •• • • • example 2 continued Step 3 Sketch a line of best fit. Draw a line that splits the data evenly above and below. • Step 4 Identify the equation for the data. end • • • • •• • • • Example 3: Anthropology Application Anthropologists can use the femur, or thighbone, to estimate the height of a human being. The table shows the results of a randomly selected sample. (a)Make a scatter plot for this set of data. (b)Identify the correlation (c)sketch a line of best fit (d)find its equation. example 3 continued a. Make a scatter plot of the data with femur length as the independent variable. • •• • • •• • Fitting3 with Linear Models Continued 1-4 CurveExample b. Find the correlation coefficient r and the line of best fit. Interpret the slope of the line of best fit in the context of the problem. Enter the data into lists L1 and L2 on a graphing calculator. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit is h ≈ 2.91l + 54.04. Holt McDougal Algebra 2 Example 3 with Continued Linear Models 1-4 Curve Fitting What does the slope indicate about problem? Holt McDougal Algebra 2 Example 3 Continued c. A man’s femur is 41 cm long. Predict the man’s height. The equation of the line of best fit is h ≈ 2.91l + 54.04. Use the equation to predict the man’s height. For a 41-cm-long femur, h ≈ 2.91(41) + 54.04 Substitute 41 for l. h ≈ 173.35 The height of a man with a 41-cm-long femur would be about 173 cm. end Example 4 The gas mileage for randomly selected cars based upon engine horsepower is given in the table. a. Make a scatter plot of the data with horsepower as the independent variable. •• •• • •• • • • with Linear Models Example 4 Continued 1-4 Curve Fitting b. Find the correlation coefficient r and the line of best fit. Interpret the slope of the line of best fit in the context of the problem. Enter the data into lists L1 and L2 on a graphing calculator. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit is y ≈ –0.15x + 47.5. Holt McDougal Algebra 2 Example 4 Continued The slope is about –0.15, so for each 1 unit does the slope indicatedrops ? increase What in horsepower, gas mileage ≈ 0.15 mi/gal. c. Predict the gas mileage for a 210-horsepower engine. The equation of the line of best fit is y ≈ –0.15x + 47.5. Use the equation to predict the gas mileage. For a 210-horsepower engine, y ≈ –0.15(210) + 47.50. Substitute 210 for x. y ≈ 16 The mileage for a 210-horsepower engine would be about 16.0 mi/gal. end Exit Question: complete on graph paper attached to Exit Question sheet (a)Make a scatter plot for this set of data using your calculator (b)find its equation.