Lesson 10
Putting It All Together
- Let’s interpret data
10.1: Which One Doesn’t Belong: Data Correlations
Which one doesn’t belong?
\(x\) | \(y\) |
---|---|
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 |
After analyzing the data, Elena concludes:
- An estimate for the correlation coefficient for the line of best fit is \(r = \text-0.98\).
- Energy consumption and the price of electric bills have a positive relationship.
- Energy consumption and the price of electric bills have a weak relationship.
- 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 |
- Use technology to create a scatter plot, a line of best fit, and the correlation coefficient.
- Is there a relationship between players’ level of confidence in winning and the amount of points they score in a game? Explain your reasoning.
- How many points does the linear model predict a player will score when his or her confidence is at a 4?
- Which players performed worse than the model predicted?
- Did Diego score better or worse than the linear model predicts?