1. 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

2. 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.

3. 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.

4. GOAL:

5. SCATTER PLOTS:
We must be able to provide domain, range and ordered pairs.

6. Positive Correlation:
CORRELATIONS: In any data we can have three types of correlation: y
Positive Correlation: x
Our data increases from left to right.

7. Negative Correlation:y x
Our data decreases from left to right.

8. No Correlation: y x
Our data does not have any pattern.

9. Correlation Coefficient (r):

10. 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.
Weight of a 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

11. 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.

12. Positive Correlation Trend Line
Procedure 1: Scatter Plot
Age (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
54.9
Positive Correlation Trend Line 60 50
Weight (lbs) 40 30 20 10 2 4 6 8 10 12
Age (Months)

13. 𝒚 =5.2𝒙 – 3.7 Procedure 2: Write an equation of the Trend
Using A(4, 17.1) and B(8, 37.9), points on the positive correlation line, we find the slope
Age
Weight 1
2.5 2
7.6 3
12.5 4
17.1 6
24.3 8
37.9 10
49.2 12
54.9
m= 𝟑𝟕.𝟗 −𝟏𝟕.𝟏 𝟖−𝟒 = 𝟐𝟎.𝟖 𝟒 = 5.2
Using one of the two points and the point-slope form equation: 𝒚- 𝒚𝟏 = m(𝒙-𝒙𝟏) we get:
𝒚 =5.2(𝒙 - 4)
𝒚 =5.2𝒙 – 20.8
𝒚 =5.2𝒙 –
𝒚 =5.2𝒙 – 3.7

14. Thus a 7-month-old panda will weight about 32.7 lbs.
Procedure 3: Estimate the weight of the 7-month-old panda
Using the found equation of the Trend Line:
𝒚 =5.2𝒙 – 3.7
and letting x = 7 months,
we get:
𝒚 =5.2(7) – 3.7
𝒚 =36.4 – 
𝒚 =32.7
Thus a 7-month-old panda will weight about 32.7 lbs.

15. 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
Temp 35 46 33 52 30 67 25 76 43 32 40 37 39 44

16. Negative Correlation Trend Line
Procedure 1: Scatter Plot
Latitude
(x)
Temp (y) 35 46 33 52 30 67 25 76 43 32 40 37 39 44 80 70 60 50 40
Temperature (o F) 30 20 10
Negative Correlation Trend Line 20 25 30 35 40 45 50
Latitude (o N)

17. 𝒚 = -3𝒙+157 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
(x)
(y) 35 46 33 52 30 67 25 76 43 32 40 37 39 44
m= 𝟑𝟕−𝟔𝟕 𝟒𝟎−𝟑𝟎 = −𝟑𝟎 𝟏𝟎 = - 3
Using one of the two points and the point-slope form equation: 𝒚- 𝒚𝟏 = m(𝒙-𝒙𝟏) we get:
𝒚- 67 = -3 (𝒙 - 30)
𝒚- 𝟔𝟕 =-3𝒙+𝟗𝟎
𝒚 =-3𝒙
𝒚 = -3𝒙+157

18. Thus at latitude of 50o N the temperature will be about 7o F.
Procedure 3: Estimate the temperature of the 50oN:
Using the found equation of the Trend Line:
𝒚 = -3𝒙+157
and letting x = 50o N of latitude
we get:
𝒚 =-3(50)+𝟏𝟓𝟕
𝒚 = – 
𝒚 =7
Thus at latitude of 50o N the temperature will be about 7o F.

19. VIDEOS:
Scatter Plots

20. CLASSWORK: Page
Problems: As many as needed to master the concept