relationship between test conditions and time to failure using linear regression


New Member
Hello all, I'm Tom and i've decided it'd be a good idea to join this forum as i'm just about to start my third year of my degree in september; a Beng in Materials Science and Engineering, and my third year project will involve quite a bit of statistics!

I'm working on a problem at the moment, and to be honest i dont know where to start...

the question reads 'using the data contained overleaf, estimate using the least squares technique, the following relationship between the tests conditions and time to failure': (image of equation is attached)

  • t_0.5j is the median time to failure at test condition j
  • ST_j is the stress at test condition j
  • T_j is the temperature at test condition j

the dataset is for the time to failure of a steel alloy with varying stress levels, set at a fixed temperature. i have attached this, together with the work that ive started to do.

my problem is that i have to find A_1, A_2 and A_3 in the equation, but i dont know where to start?? how does the least squares method link up to the equation, and hence A_1, A_2 and A_3?

I'm not looking for the problem to be solved here, but just the method in which i can derive the answer myself.

I missed most of the lectures i had on statistics due to my father being diagnosed with brain cancer, so i wanted to spend those particular days at home before he passed away :(

many thanks, and i hope i can contribute to the forum if anyone needs any engineering knowledge/advice :D