Question: Following the machining process the components are to be hardened and then tempered. As part of the design process a sample of eight components was tempered at different temperatures with the following results:

(a) Draw a scatter diagram of this data and calculate the correlation coefficient. Comment on the nature of the relationship between temperature and hardness.

(b) Use least-squares linear regression analysis to establish an equation with which hardness can be predicted from temperature for this particular steel.

(c) Use the equation found above to estimate the hardness values for temperatures of 260°C and 370°C.

(d) Comment on the accuracy and reliability of estimates that may be obtained using the preceding analysis.