Suppose we have driving data for a number of ages of drivers. Assume the data we have gives the distance away a road sign is legible to a driver of a given age. We have the following training set to use for Linear Regression. Use this information to answer the following questions. Age Distance in feet _____________________________________ 20 575 25 525 45 425 55 400 65 350

1. If we only use the first two data points in the training set (ages 20 and 25) then what is the equation of the line found by using Linear Regression? Write your line in the form y=mx+b where x represents the age, y the distance the sign is visible and you provide the correct values of the slope m and y-intercept b. Justify your answer.
2. Use your line from (1) to predict the distance a person of age 45 can see the sign. Explain why it is quite different from the value in the table for a 45 year old.
3. If we use Linear Regression to find the line which best fits all 5 data points in the training set then we get the line y = -5.54 x + 677.7 Use this line to predict the distance a 50 year old person can see a road sign. Again x represents the age and y the distance.
4. If we add a data point to our training set for a person 50 years old who can see the sign at 370 feet, how do you expect the line from (3) to change? Explain your reasoning.