EXAMPLE 6 Calculating the regression coefficients and

  1. Find the value of the regression coefficients and for the temperature data in Table 3.
  2. Write out the equation of the regression line for the temperature data.
  3. Clearly explain the meaning of the regression equation.

Solution

  1. We will outline the steps used in calculating the value of using the temperature data.
    • Step 1 Calculate the respective sample means and . We have already done this in Example 4 (page 193): and .
    • Step 2 Calculate the respective sample standard deviations and . We have already done this in Example 4: and .
    • Step 3 Find the correlation coefficient . This was computed in Example 4: .
    • Step 4 Combine the statistics from Steps 2 and 3 to calculate :

    • Step 5 Use the statistics from Steps 1–4 to calculate :

  2. Thus, the equation of the regression line for the temperature data is

  3. Because and represent high and low temperatures, respectively, this regression equation is read as follows: “The estimated high temperature for an American city is 1.4 times the low temperature for that city plus 8 degrees Fahrenheit.”

NOW YOU CAN DO

Exercises 7–12 and 13a–24a.