A study was done for a vitamin supplement that claims to shorten the length of the common cold. The data the scientists collected from ten patients in an early study is shown in the table below.   

1. Describe the association.

   Step 1(a):

   Graph the points.

   Step 2(a):

   From the graph, determine if the scatterplot is linear or curved.

   Hint (a):

   Is the slope positive or negative?

   More Help (a):

   How close are the data points to your line or curve?

   Are there any outliers?

2. Model the data with a line of best fit. According to your model, how many days do you expect a cold to last for a patient taking the supplement for $1.5$ months?

   Hint (b):

   How long do you predict a cold will last for a person who has not taken the supplement?

   Step 1(b):

   Estimate the line of best fit. Remember that the equation of your line does not have to exactly match what the table shows.

   Step 2(b):

   Find the $y$-intercept and slope to write the equation of your line.

   Step 3(b):

   Substitute $1.5$ for $x$.

3. Calculate the residual for 1.5 months. Interpret the residual in the context of the problem.

   Hint (c):

   The residual is the difference between the actual value and the predicted value.

4. Interpret the $y$-intercept in context.

• Hint (d):

  How long do you predict a cold to last for a person who has not taken any supplement?