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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. Today’s Objectives:

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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?

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Line of Best Fit 1.Prepare a scatter plot of the data on graph paper. 2.Using a ruler, position the ruler so that the plotted points are as close to the ruler’s edge as possible. 3.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. Women Men

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Line of Best Fit

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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.

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Scatterplot To Predict Regression Line

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How to Save a Life Call-to-shock time (min.) Survival rate (%)

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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. Call-to-shock time (min.) Survival rate (%)

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Heights of Men and Women

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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.

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Tie The Knot

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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.

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Diameter vs. Height

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

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

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# of Students

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

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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.

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Real-Estate Pricing

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Predictions Using your line of best fit to predict… a)Woodstock, New York, is located 95 miles from New York City, determine the price of a 3-bedroom home in Woodstock. b)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.)

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Predictions

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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!

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Scatterplot To Predict Regression Line

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