Here are Elena’s representations of the data set. 

Line and 21 data points on grid. Horizontal axis, energy, kilowatts, from 0 to 1400 by 200’s. Vertical axis, price of electric bill, dollars, from 0 to 300 by 20’s. Data points listed in table above. Line starts at 500 comma 18, moves upwards and to the right passing near 600 comma 50, 900 comma 170, and 1250 comma 290. 8 data points are close to and below line. 6 points fall on the line. 7 data points are close to and above the line.

After analyzing the data, Elena concludes:

1. An estimate for the correlation coefficient for the line of best fit is .
2. Energy consumption and the total amount charged for the electricity have a positive relationship.
3. Energy consumption and the total amount charged for the electricity 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.

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.

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?