4%2D5 Scatter Plots and Lines of Fit

[Pages:24]4-5 Scatter Plots and Lines of Fit Determine whether each graph shows a positive, negative , or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

62/87,21 The graph shows a positive correlation. As the time you practice free throws increases, the number of free throws you will make increases.

62/87,21 The graph shows a positive correlation. As the temperature gets warmer, the more lemonade you will sell.

CCSS SENSE-MAKING The table shows the median age of females when they were first married.

Year

Age

1996

24.8

1997

25.0

1998

25.0

1999

25.1

2000

25.1

2001

25.1

2002

25.3

2003

25.3

2005

25.5

2006

25.9

Source: U.S. Bureau of Census

D Make a scatter plot and determine what relationship exists, if any, in the data. Identify the independent and the

dependant variables.

E Draw a line of fit for the scatter plot. eSolutions Manual - Powered by Cognero

F Write an equation in slope-intercept form for the line of fit.

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 D Make a scatter plot and determine what relationship exists, if any, in the data. Identify the independent and the dependant variables. 4-5 Scatter Plots and Lines of Fit E Draw a line of fit for the scatter plot. F Write an equation in slope-intercept form for the line of fit. G Predict what the median age of females when they are first married will be in 2016. H Do you think the equation can give a reasonable estimate for the year 2056? Explain.

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a and b.

The graph shows a positive correlation. The independent variable is the year and the dependent variable is the median age of females when they were first married. F Sample answer: Using (1996, 24.8) and (2006, 25.9) and rounding, y = 0.11x 194.8 G Sample answer: y = 0.11x + 25.24 y = 0.11(16) + 25.24 y = 1.76 + 25.24 y = 27 So, the median age of females when they are first married in 2016 will be 27. e . Sample answer: y = 0.11x + 25.24 y = 0.11(56) + 25.24 y = 6.16 + 25.24 y = 31.4 Yes, the equation can give a reasonable estimate. According to the equation, the median age of females in 2056 when they are first married would be 31.4, which is likely.

Determine whether each graph shows a positive, negative , or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

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62/87,21

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The graph shows a positive correlation. As the number of tickets you buy increases, the more game prizes you will

y = 0.11(56) + 25.24 y = 6.16 + 25.24 y = 31.4 4-5 SYceast,tethrePelqoutastaionndcLaningeisveofa Freiatsonable estimate. According to the equation, the median age of females in 2056 when they are first married would be 31.4, which is likely. Determine whether each graph shows a positive, negative , or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

62/87,21 The graph shows a positive correlation. As the number of tickets you buy increases, the more game prizes you will win.

62/87,21 The graph shows a negative correlation. As the NBA player gets taller, his 3-point shooting percentage gets lower.

62/87,21 The graph shows a positive correlation. As the number of years of formal education you receive increases, the higher your salary will be.

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62/87,21 4-5 STchaettgerrapPhlosthsoawnsdaLpionseitsivoefcFoirtrelation. As the number of years of formal education you receive increases, the

higher your salary will be.

62/87,21 There is no correlation. The various vehicles give too many varying results for there to be a correlation between the speed of the vehicle and the miles per gallon.

0,/. Refer to the scatter plot of gallons of milk consumption per person for selected years.

D Use the points (2, 21.75) and (4, 21) to write the slope-intercept form of an equation for the line of fit. E Predict the milk consumption in 2015. F Predict in what year milk consumption will be 10 gallons. G Is it reasonable to use the equation to estimate the consumption of milk for any year? Explain.

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a. Find the slope of the line containing the given points.

Use the slope and either of the two points to find the y -intercept.

Write the equation in slope-intercept form for the line of fit.

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4-5 Scatter Plots and Lines of Fit Write the equation in slope-intercept form for the line of fit.

b.6XEVWLWXWHIRUx in the equation found in part a to predict how much milk will be consumed in 2020.

In 2020, about 15 gallons of milk will be consumed. c. Substitute 10 for y into the equation from part a to find the year that milk consumption will be 10 gallons.

In the year 2033, the milk consumption will be 10 gallons. d. Yes; if the current trend continues, the consumption of milk will continue to decrease.. )227%$// Use the scatter plot.

D Use the points (5, 71,205) and (9, 68,611) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot. E Predict the average attendance at a game in 2020. F Can you use the equation to make a decision about the average attendance in any given year in the future? Explain.

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a. Find the slope of the line containing the given points.

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F Can you use the equation to make a decision about the average attendance in any given year in the future? Explain. 62/87,21 4-5 Scatter Plots and Lines of Fit a. Find the slope of the line containing the given points.

Use the slope and either of the two points to find the y -intercept.

Write the equation in slope-intercept form for the line of fit.

b.6XEVWLWXWHIRUx in the equation from part a.

The average attendance at a Buffalo Bills game in 2020 will be 61,478 people. c. No you cannot use this equation to make predictions about future attendance because the average attendance will fluctuate with other variables such as how good the team is that year. CCSS SENSE-MAKING The Body Mass Index (BMI) is a measure of body fat using height and weight. The heights and weights of twelve men with normal BMI are given in the table shown.

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D Make a scatter plot comparing the height in inches to the weight in pounds.

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c. No you cannot use this equation to make predictions about future attendance because the average attendance will fluctuate with other variables such as how good the team is that year.

4-5SCcCatSteSrSPElNotSsEa-nMdALKinIeNsGofTFhiet Body Mass Index (BMI) is a measure of body fat using height and weight. The heights and weights of twelve men with normal BMI are given in the table shown.

D Make a scatter plot comparing the height in inches to the weight in pounds. E Draw a line of fit for the data. F Write the slope-intercept form of an equation for the line of fit. G Predict the normal weight for a man who is 84 inches tall. H A man?s weight is 188 pounds. Use the equation of the line of fit to predict the height of the man.

62/87,21 a.?b.

c. Answers will vary depending on which points the student picks. Sample answer: Choose two points on the best fit line: (62, 115) and (69, 147). Calculate the slope.

eSolutUionses Mthaenusallo-pPeowanerdedeibtyhCerogonfertohe two points to find the y -intercept.

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4-5 Scatter Plots and Lines of Fit Use the slope and either of the two points to find the y -intercept.

y = 4.57x ? 168.33 G Let x = 84 inches. Substitute this into the equation.

Sample answer: 215.6 lb H If a man?s weight is 188 lbs, substitute y = 188 and find x.

Sample answer: about 78 in.

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