A recent survey investigated the relationship between the number of traffic tickets a person has received and the cost of the person's car insurance. The scatter plot displays the relationship.

A scatterplot. Horizontal, from 0 to 12, by 1’s, traffic tickets. Vertical, from 0 to 1000, by 100’s, car insurance, dollars. 16 dots, trend linearly upward and right, dot 1 at about 0 comma 125 and dot 16 at 12 comma 900.

The line that models the data is given by the equation \(y = 73x+146.53\), where \(x\) represents the number of traffic tickets, and \(y\) represents the cost of car insurance.

1. The slope of the line is 73. What does this mean in this situation? Is it realistic?
2. The \(y\)-intercept is \((0, 146.53)\). What does this mean in this situation?

Technology required.

A survey wanted to determine if there was a relationship between the number of joggers who used a local park for exercise and the temperature outside. The data in the table display their findings. 

Use graphing technology to create a scatter plot of the data.

1. Is a linear model appropriate for this data? Explain your reasoning. 
2. If a linear model seems appropriate, create the line of best fit. Round to two decimal places. 
3. What is the slope of the line of best fit, and what does it mean in this context? Is it realistic?
4. What is the \(y\)-intercept of the line of best fit, and what does it mean in this context? Is it realistic?

The data for a local hospital is collected to examine the relationship between the length of a person's stay in the hospital in days, \(x\), and the amount owed for the hospital bill, \(y\). The line of best fit for the data is \(y=1,\!899.66x+852.81\).

1. Find the residuals for the three patients who were in the hospital for 6 days: \((6, 14320)\), \((6, 7900)\), and \((6, 13998)\).
2. Compare the residuals for the three patients. How are they similar? How are they different? What does the information about the residuals for the three patients tell you about their hospital bills? 

Select all the values for \(r\) that indicate a strong, negative relationship for the line of best fit.

Noah collects data to investigate the relationship between the number of runs scored by his favorite professional baseball team, \(x\), and the number of runs scored by his high school baseball team, \(y\). Which value for the correlation coefficient is most likely to match a line of best fit of the form \(y = mx + b\) for this situation?

Noah creates a scatter plot showing the relationship between the number of free throws made in a basketball game and the number of points scored. The correlation coefficient for the line of best fit is 0.76.

1. Are they correlated? Explain your reasoning.
2. Do either of the variables cause the other to change? Explain your reasoning.

A news headline claims that “Essential Oils Cause Hormone Levels to Drop.” They show a scatter plot displaying a weak, negative relationship (\(r = \text{-}0.13\)) between essential oil use and hormone levels.

1. What is wrong with this claim?
2. What is a better headline for this information?

Technology required.

Data in the table shows the relationship between the average number of social network notifications that students receive during one class, \(x\), and average test score for that class, \(y\).