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Unit 4 (2-Variable Quantitative): Scatter Plots Standards: SDP 1.0 and 1.2 Objective: Determine the correlation of a scatter plot

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Scatter Plot A scatter plot is a graph of a collection of ordered pairs (x,y). The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

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Scatter Plots Summarizes the relationship between two quantitative variables. Horizontal axis represents one variable and vertical axis represents second variable. Plot one point for each pair of measurements.

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Positive Correlation If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION. This means that both are going up, and they are related.

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Positive Correlation If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation. Age12345678 Height “ 2531343640414755

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Negative Correlation If the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

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Negative Correlation If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation. Age of car 12345 Value$30,000$27,00 0 $23,50 0 $18,70 0 $15,35 0

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No Correlation If there seems to be no pattern, and the points looked scattered, then it is no correlation. This means the two are not related.

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No Correlation If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

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A number, r, from -1 to 1 that measures how well a line fits a set of data points. -1 – strong negative correlation -0.5 – weak negative corr. 0 – no correlation 0.5 – weak positive corr. 1 – strong positive corr. Correlation Coefficient

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Strength

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Put the correlation coefficients in order from weakest to strongest Ex 1: 0.87, -0.81, 0.43, 0.07, -0.98 Ex 2: 0.32, -0.65, 0.63, -0.42, 0.04 0.07, 0.43, -0.81, 0.87, & -0.98 0.04, 0.32, -0.42, 0.63, & -0.65

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Match the Correlation Coefficient to the graph Graph Correlation Coefficients -0.5 0 0.5 1

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Match the Correlation Coefficient to the graph Graph Correlation Coefficients -0.5 0 0.5 1

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Match the Correlation Coefficient to the graph Graph Correlation Coefficients -0.5 0 0.5 1

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A.The number of hours you work vs. The amount of money in your bank account B. The number of hours workers receive safety training vs. The number of accidents on the job. C. The number of students at Hillgrove vs. The number of dogs in Atlanta Positive, Negative, or No Correlation?

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Some Types of Regression Linear Regression (straight line form) Quadratic Regression (parabolic form) Cubic Regression (cubic form)

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Scatterplots Which scatterplots below show a linear trend? a) c)e) b) d)f) Negative Correlation Positive Correlation Constant Correlation

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Best Fit Line By Hand The table shows the number of people y who attended each of the first seven football games x of the season. Approximate the best-fitting line for the data. Steps: 1) Draw a scatter plot. 2) Sketch the best-fitting line. 3) Choose 2 data points on the best-fit line and solve for the slope. 4) Use one of the points and the slope to solve for b in y = mx + b. x 1 2 3 4 5 6 7 y722763772826815857897

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Year Sport Utility Vehicles (SUVs) Sales in U.S. Sales (in Millions) 1991 1992 1993 1994 1995 1996 1997 1998 1999 0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Objective - To plot data points in the coordinate plane and interpret scatter plots.

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1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2001.

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Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis.. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 90 min.

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Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TVHomework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 120 min. 90 min. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30

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Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30 Trend is decreasing. Trend appears linear. Negative correlation.

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Best Fit Line Using A TI-30x Calculator 1)Press [2 nd ], then [Stat] 2)Select 2-VAR 3)Press [Data] 4)X1 = first data point’s x Y1 = first data point’s y 5) Keep pressing down arrow to go to new points 6) Press [STATVAR] 7) a = slope, b = y-intercept

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Best Fit Line Using A TI-84 Graphing Calculator See Handout

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Example 1: Consumer Debt The table shows the total outstanding consumer debt (excluding home mortgages) in billions of dollars in selected years. (Data is from the Federal Reserve Bulletin.) Let x = 0 correspond to 1985. a) Using a graphing calculator, draw the scatterplot. Interpret the plot: 1.Form 2.Strength 3.Direction Year19851990199520002003 Consumer Debt585789109616931987

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Example 1: Consumer Debt (cont) b) Find the regression equation appropriate for this data set. Round values to two decimal places. c) Find and interpret the slope of the regression equation in the context of the scenario. Year19851990199520002003 Consumer Debt585789109616931987

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Example 1: Consumer Debt (cont) d) Find the approximate consumer debt in 1998. e) Find the approximate consumer debt in 2008. 1501.52 billion 2300.11 billion

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Example 1: Consumer Debt (cont) f) Using the regression equation, predict the year when consumer debt will reach 2,500 billion dollars. 25.5 years or 2010 and a 1/2 year

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Example 2: Health The table below shows the number of deaths per 100,000 people from heart disease in selected years. (Data is from the U.S. National Center for Health Statistics.) Let x = 0 correspond to 1960. a) Using a graphing calculator, draw the scatterplot. Interpret the plot: 1.Form 2.Strength 3.Direction Year196019701980199020002002 Deaths559483412322258240

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Example 2: Health (cont) b) Find the regression equation appropriate for this data set. Round values to two decimal places. c) Find and interpret the slope of the regression equation in the context of the scenario.

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Example 2: Health (cont) d) Find an approximation for the number of deaths due to heart disease in 1995. e) Predict the number of deaths from heart disease in 2008. 635 194

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