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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models Cover 1.4 if time; non-Algebra 2 objective Gasaway going over briefly: get students to narrow down, positive verse negative correlation just by appearance and how to do on calculator Teaching note

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Bell Ringer Find each slope: 1. (5, – 1), (0, – 3)2. (8, 5), ( – 8, 7)

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Fit scatter plot data using linear models with and without technology. Use linear models to make predictions. 1.4 Objectives A line of best fit may also be referred to as a trend line.

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models FOUR KINDS OF CORRELATIONS (YOU WILL LEARN ABOUT IN TRANSITION) Positive Correlation Negative Correlation Constant Correlation No Correlation

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models **Practice how to use calculator with following slide ** make sure all steps are included for students **Need uncooked spaghetti for this unit (optional). Be patient, allow students time to copy question and data. Offer students graph paper Teaching note:

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Holt McDougal Algebra 2 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) 2 nd 8) y= plot1 on TYPE X list L1 & Y list L2 mark (select on) GRAPH

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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. That’s to much work with paper & pencil How to: Calculator data entry continuedcontinued Enter ______ in list L1 by pressing STAT and then 1. Enter _______ in list L2 by pressing Make scatter plot in the following way: Press 2 nd Y= PLOT 1 set up desired type when done, press GRAPH Tables: ACT

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o o 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?)

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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.

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models Teaching note: following slide Do not advance to next slide until students have had time to finish previous slide

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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

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Step 3 Sketch a line of best fit. Draw a line that splits the data evenly above and below. example 2 continued Step 4 Identify the equation for the data. end

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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.

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a. Make a scatter plot of the data with femur length as the independent variable. example 3 continued

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models 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. Example 3 Continued

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models Example 3 Continued What does the slope indicate about problem?

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c. A man’s femur is 41 cm long. Predict the man’s height. Substitute 41 for l. The height of a man with a 41-cm-long femur would be about 173 cm. h ≈ 2.91(41) + 54.04 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 ≈ 173.35 Example 3 Continued end

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Example 4 a. Make a scatter plot of the data with horsepower as the independent variable. The gas mileage for randomly selected cars based upon engine horsepower is given in the table.

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models 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. Example 4 Continued

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c. Predict the gas mileage for a 210-horsepower engine. Substitute 210 for x. The mileage for a 210-horsepower engine would be about 16.0 mi/gal. y ≈ –0.15(210) + 47.50. 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 ≈ 16 Example 4 Continued The slope is about –0.15, so for each 1 unit increase in horsepower, gas mileage drops ≈ 0.15 mi/gal. What does the slope indicate ? end

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Holt McDougal Algebra 2 1-4 Curve Fitting with Linear Models Teaching note: Exit Question long

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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.

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