5. The following table reports temperatures measured at various altitudes. Use this data to answer the following questions. An altitude of 2,456 feet is written 2.456 for this problem.
Altitude is given in thousands of feet.
Altitude: 3, 10, 14, 22, 28, 31, 33
Temperature: 57, 37, 24, -5, -30, -41, -54
(a) Find the amount of variation in the temperature that can be explained by the altitude. Include only the one variable (and its value) that is important to this explanation. (4 points)
(b) Determine whether there is a linear correlation between altitude and temperature. Include every variable and all work that is important to make this decision. (12 points)
(c) Write the regression model for this data. Use correct notation. (5 points)
(d) Make a best prediction for the temperature at an altitude of 25,000 feet. (4 points)
(Check to see if your answer makes sense.)
(e) Write a sentence that interprets the answer from part (d). (5 points)