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Today’s Objectives:

Today’s Objectives:. Get out your Homework ! You will be able to predict an outcome based on the least-squares method. You will be able to verbalize the meaning of slope and y-intercept of various scenarios. Warm Up.

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Today’s Objectives:

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  1. Today’s Objectives: Get out your Homework! You will be able to predict an outcome based on the least-squares method. You will be able to verbalize the meaning of slope and y-intercept of various scenarios.

  2. Warm Up A regression line is sometimes referred to as the “line of best fit.” Considering what you have learned in the past few lessons, why do you think it is called that? Is there really only one line of best fit?

  3. Line of Best Fit Prepare a scatter plot of the data on graph paper. Using a ruler, position the ruler so that the plotted points are as close to the ruler’s edge as possible. Find two points that you think will be on the "best-fit" line. Different people may choose different points. A rule of thumb is to try to get an equal number of points above the line as below.

  4. Line of Best Fit 4.  Calculate the slope of the line through your two points (rounded to three decimal places). . 5.  Write the equation of the line.  This equation can now be used to predict information that was not plotted in the scatter plot.  For example, you can use the equation to find the height of a husband based upon a his wife’s height of 57 inches.

  5. Line of Best Fit. Different people may choose different points and arrive at different equations. All of them are "correct", but which one is actually the "best"?  To determine the actual "best" fit, we will use a graphing calculator. This line is our regression line, and it IS the line of best fit.

  6. Scatterplot STATEDIT L1: Explanatory/independent/x L2: Response/dependent/y ZOOM9:ZoomStat STAT arrow right to CALC choose 8:LineReg(a+bx) Type L1,L2,Y1ENTER GRAPH Press TRACE arrow down Type in new value and hit ENTER Regression Line To Predict

  7. How to Save a Life Make a scatterplot of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line (round to the nearest hundredth place)

  8. How to Save a Life What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  9. Heights of Men and Women Make a scatterplot of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line.

  10. Heights of Men and Women What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  11. Tie The Knot Find the data that you found when tying the rope into knots. Everyone’s data will be different. Be prepared to share your data with the class. Make a scatterplot of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line. What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  12. Diameter vs. Height A biologist is studying the relationship between a tree’s diameter and its height. She records the following data for 7 different trees. Copy this chart into your notes and create a scatterplot by hand.

  13. Diameter vs. Height Make a scatterplot in your calculator of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line. What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  14. Predictions Using your line of best fit estimate, to the nearest foot, the height of a tree given that its diameter is... 6.3 inches 14 inches. This type of calculation is called extrapolating; we are using a model to predict outside of our data set.

  15. # of Students The table below shows the number of students in Arlington High School as a function of the number of years since 2000

  16. # of Students Make a scatterplot in your calculator of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line. What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  17. Predictions Using your line of best fit to predict… the population of Arlington High School in the year 2012. determine between which two consecutive whole number years the population reaches 4500

  18. Real-Estate Pricing A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records data for 6 homes shown below.

  19. Real-Estate Pricing Make a scatterplot in your calculator of the following table. Find the correlation coefficient, . Use your calculator to draw the regression line. Write out the equation of the regression line. What is the slope of the line? Explain in words what the slope means in the setting. What is the y-intercept? Explain in words what the y-intercept means in the setting.

  20. Predictions Using your line of best fit to predict… Woodstock, New York, is located 95 miles from New York City, determine the price of a 3-bedroom home in Woodstock. Using your model, determine the price of a 3-bedroom home in New York City. (Hint: think about the value of x when you are in New York City.)

  21. Predictions Using your line of best fit to predict… Using tables, determine, to the nearest mile, the distance from New York City a home would be if its selling price were exactly $500,000. Using tables, determine, to the nearest mile, the distance from New York City a home would be if its selling price were $0. Why is your answer to part unreasonable?

  22. Extrapolation When we use extrapolation with linear models we can sometimes get unreasonable answers. This is because we are using the model with explanatory variable values for which the model does not apply. Extrapolation is risky!

  23. Scatterplot STATEDIT L1: Explanatory/independent/x L2: Response/dependent/y ZOOM9:ZoomStat STAT arrow right to CALC choose 8:LineReg(a+bx) Type L1,L2,Y1ENTER GRAPH Press TRACE arrow down Type in new value and hit ENTER Regression Line To Predict

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