5.7 SCATTER PLOTS AND TREND LINES:

5.7 SCATTER PLOTS AND TREND LINES:

Scatter Plot: a graph that relates two different sets of data by displaying them as ordered pairs (x, y).

Correlation: The relationship/trend found in any given data.

Trend line: Line on a scatter plot, drawn near the points, that shows a correlation

Interpolation: The act of estimating a value between two known values.

Extrapolation: The act of predicting a value outside of the range of known values.

Line of Best Fit: Line that shows the most accurate relationship between two sets of data.

Correlation Coefficient(r): a number from -1 to 1 that tells us how closely the equation models the data.

Causation: A change in one quantity causes a change in a second quantity.

GOAL:

SCATTER PLOTS:

We must be able to provide domain, range and ordered pairs.

CORRELATIONS: In any data we can have three types of correlation:

Positive Correlation:

Our data increases from left to right.

y

x

Negative Correlation:

Our data decreases from left to right.

y

x

No Correlation:

Our data does not have any pattern.

x

y

Correlation Coefficient (r):

Whenever we are given data/information/ordered pairs, we must be able to provide certain details:

Ex: Make a scatter plot of the data, provide the type of relationship it represents and the approximate weight of a 7-month-old panda.

Age (months) 1 2 3 4 6 8 10 12

Weight (lbs) 2.5 7.6 12.5 17.1 24.3 37.9 49.2 54.9

Weight of a Panda

To answer the questions on the panda task we must do three procedures:

Procedure 1: Create a Scatter Plot

Procedure 2: Write an Equation of the Trend of the Line

Procedure 3: Estimate the weight of a 7-month-old panda.

Procedure 1: Scatter PlotAge (x) 1 2 3 4 6 8 10 12

Weight(y) 2.5 7.6 12.5 17.1 24.3 37.9 49.2 54.9W

eigh

t (lb

s)

Age (Months)2 4 6 8 10 12

10

20

30

40

50

60Positive

Correlation Trend Line

Procedure 2: Write an equation of the TrendAge Weigh

t

1 2.5

2 7.6

3 12.5

4 17.1

6 24.3

8 37.9

10 49.2

12 54.9

Using A(4, 17.1) and B(8, 37.9), points on the positive correlation line, we find the slope m= = = 5.2

Using one of the two points and the point-slope form equation: - = m(-) we get: -17.1 =5.2(- 4) -17.1 =5.2– 20.8 =5.2– 20.8 +17.1

=5.2– 3.7

Procedure 3: Estimate the weight of the 7-month-old panda

=5.2– 3.7 Using the found equation of the Trend Line:

and letting x = 7 months,

we get: =5.2(7)– 3.7

=36.4– 3.7 =32.7

Thus a 7-month-old panda will weight about 32.7 lbs.

YOU TRY IT: Use the data below to create a scatter plot, provide the relationship and approximate the daily temperature in January at a latitude of 50o N.

Latitude Temp35 4633 5230 6725 7643 3240 3739 44

Procedure 1: Scatter PlotTe

mpe

ratu

re (o

F)

Latitude (o N)20 25 30 35 40 45

10

20

30

40

50

60

Negative Correlation Trend Line

Latitude (x)

Temp (y)

35 46

33 52

30 67

25 76

43 32

40 37

39 44

70

80

50

Procedure 2: Write an equation of the Trend

Using A(30, 67) and B(40, 37), points on the negative correlation line, we find the slope m= = = - 3

Using one of the two points and the point-slope form equation: - = m(-) we get: -67 = -3 (- 30) - =-3 =-3 + 90 + 67

= -3157

(x) (y)35 46

33 52

30 67

25 76

43 32

40 37

39 44

Procedure 3: Estimate the temperature of the 50oN:

= -3157Using the found equation of the Trend Line:

and letting x = 50o N of latitude

we get: =-3(50)

= –150 + 157 =7

Thus at latitude of 50o N the temperature will be about 7o F.

VIDEOS:Scatter Plots

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-slope-intercept/v/fitting-a-line-to-data

CLASSWORK:

Page 338-339

Problems: As many as neededto master the concept