Lesson 10

Putting It All Together

  • Let’s interpret data

10.1: Which One Doesn’t Belong: Data Correlations

Which one doesn’t belong? 

A

Line and 10 data points on grid.

B

Line and 13 data points on grid.

C

Line and 20 data points on grid.
 
D
\(x\) \(y\)
3 6
3.75 8.50
7.25 7.50
5.50 11
6 9
8 10.25
 

 

10.2: Electric Power

Here are Elena’s representations of the data set. 

energy (kwh) electric bill price (dollars)
500 50
560 57.60
610 65.10
675 70.25
700 74.80
755 90.66
790 92.34
836 105
892 150
940 173
932 182
 
energy (kwh) electric bill price (dollars)
967 170
999 198
1,005 201.22
1,039 215.35
1,057 217
1,100 233
1,191 284.62
1,150 256.98
1,200 289.60
1,270 292
 
Line and 21 data points on grid.

After analyzing the data, Elena concludes:

  1. An estimate for the correlation coefficient for the line of best fit is \(r = \text-0.98\).
  2. Energy consumption and the price of electric bills have a positive relationship.
  3. Energy consumption and the price of electric bills have a weak relationship.
  4. Using the linear model, the electric bill is $260 when 1,200 kWh are consumed.

What parts of Elena’s interpretation of the data do you agree with and what parts do you disagree with? Explain your reasoning.

10.3: Confident Players

Before Diego’s game, his coach asked each of his players, “On a scale of 1–10, how confident are you in the team winning the game?” Here is the data he collected from the team.

 players   confidence in winning (1–10)   number of points scored in a game
 Player A  3 2
 Diego 6 10
 Player B 10 2
 Player C 4 10
 Player D 7 13
 Player E 5 6
 Player F 8 15
 Player G 4 3
 Player H 9 15
 Player I 7 12
 Player J 1 0
 Player K 9 14
 Player L 8 13
 Player M 5 8
  1. Use technology to create a scatter plot, a line of best fit, and the correlation coefficient.
  2. Is there a relationship between players’ level of confidence in winning and the amount of points they score in a game? Explain your reasoning.
  3. How many points does the linear model predict a player will score when his or her confidence is at a 4?
  4. Which players performed worse than the model predicted?
  5. Did Diego score better or worse than the linear model predicts?

Summary