The manager of a building supply center suspects that the monthly sale of rolled insulation for installation in attics depends on the average air temperature during the month. The manager has a spreadsheet with 42 months of past data on this subject, in which the overall average monthly temperature was 49 degrees Fahr- enheit and the overall average sales of rolled insulation was 428 rolls a month. On that spreadsheet, the manager has created a column in which each month's average air temperature is multiplied by each month's sales of rolled insulation, and then these 42 numbers are summed together to create the value 873,931. In another column of the spreadsheet, the manager has squared each month's average air temperature, and then summed the 42 squared temperatures to obtain a value of 105,080.

a. Next month, the average air temperature is expected to be 35 degrees Fahrenheit. Use linear regression to predict next month's sales of rolled insulation.

b. The sum of the 42 months of average air temperature readings is 2,058 and the total sales of rolled insulation over that same time period was 17,976 rolls. The sum of the squared monthly sales of rolled insulation was 7,710,080. What percent of the variation in the sale of rolled insulation is explained by its linear relationship to average temperature during these past 42 months?

c. What is the value of the correlation coefficient between average air temperature and the sale of rolled insulation? What does this value suggest about the relation- ship between average air temperature and the sale of rolled insulation?