A materials engineer is monitoring the cooling of a specialized ceramic component. The temperature of the component, TTT ∘C^\circ\text{C}∘C, is recorded at various times, ttt minutes, after it is removed from a kiln, where 4≤t≤364 \le t \le 364≤t≤36.
The engineer calculated the regression line of TTT on ttt and found it to be
T=165.4−2.85t T = 165.4 - 2.85t T=165.4−2.85tGive an interpretation of the gradient of the regression line.
Use the regression line to estimate the temperature of the component 45 minutes after it was removed from the kiln.
Comment on the reliability of your estimate in part (b), giving a reason for your answer.
Using the regression line of TTT on ttt and the following summary statistics:
∑T=1300.8∑T2=149 856.72∑t2=5850n=12 \sum T = 1300.8 \quad \sum T^2 = 149\,856.72 \quad \sum t^2 = 5850 \quad n = 12 ∑T=1300.8∑T2=149856.72∑t2=5850n=12Show that the product moment correlation coefficient (PMCC) for these data is −0.982-0.982−0.982 to 3 decimal places.
A scatter diagram of the engineer's data shows the points distributed tightly around a straight line with a negative gradient.
With reference to both the scatter diagram and the correlation coefficient, discuss the suitability of a linear regression model to describe the relationship between ttt and TTT.
