An experiment was conducted to determine the relationship between the amount of warping y for a particular alloy and the temperature (in ° C) under which the experiment was conducted. The sample data appear in the accompanying table. Note that three observations were taken at each temperature setting.
Amount of Warping Temperature (° C)
10, 13, 12………………………….. 15
14, 12, 11………………………….. 20
14, 12, 16………………………….. 25
18, 19, 22…………………………. 30
25, 21, 20…………………………. 35
23, 25, 26…………………………. 40
30, 31, 34…………………………. 45
35, 33, 38…………………………. 50
a. Plot the data to determine whether a linear or quadratic model appears more ­appropriate.
b. Fit a linear model and display the prediction equation. Superimpose the prediction equation over the scatter diagram of y versus x.
c. Fit a quadratic model and display the prediction equation. Superimpose the quadratic prediction equation on the scatter diagram. Which fit looks better, the linear or the quadratic?
d. Predict the amount of warping at a temperature of 27° C, using both the linear and the quadratic prediction equations.