In problem 4-25 you looked at the data for a study conducted on a vitamin supplement that claims to shorten the length of the common cold. The data is shown in the table below:

1. You previously created a linear model for this data by sketching a line of best fit. Now create a model that is consistent with your classmates by determining the LSRL. Sketch the graph and the LSRL.

   Hint (a):

   Review the LSRL procedure in the previous lesson.

2. Draw the upper and lower boundary lines on the graph following the process you used in problem 4-24. What is the equation of the upper boundary line? Of the lower boundary line?

   Answer (b):

   Answer: $y = 6.16 − 1.58x$ and $y = 4.58 − 1.58x$, based on a maximum residual of $−0.79$

3. Based on the upper and lower boundary lines of your model, what do you predict is the length of a cold for a person who has taken the supplement for three months? Consider the precision of the data and use an appropriate number of decimal places in your response.

   Hint (c):

   Since the number of days the cold lasted is decreasing as the number of months taking the supplement increases,
   it would seem the length of the cold should be between $1$ and $0.5$ days.

4. How long do you predict a cold will last for a person who has taken no supplement? Interpret the y-intercept in context.

   Answer (d):

   Since the $y$-intercept is around $5.3$, the number of days a cold should last for a person who hasn't taken the supplement should be around $5.3$ days.

5. How long do you predict a cold will last for a person who has taken six months of supplements?

   Answer (e):

   Negative values in this case do not make sense. Statistical models often cannot be extrapolated far beyond the edges of the data.

6. If you have a cold, would you prefer a negative or positive residual?

• Hint (f):

  If you have a cold, your goal would be to decrease the number of days the cold lasts. Would a positive or negative residual represent a decrease in the number of days that a cold lasts?