An employee at a coffee shop hypothesizes that the harder theespresso grounds are tamped down into the portafilter before​brewing, the longer the separation time of the​ heart, body, andcrema will be. The accompanying data table shows the results ofthis experiment. The independent variable tamp measuresthe​distance, in​ inches, between the espresso grounds and the topof the portafilter. The dependent variable time is the number ofseconds the​ heart, body, and crema are separated. Complete parts​(a) through​ (f) below.

Shot   Tamp   Time
1   0.20   15
2   0.55   15
3   0.25   12
4   0.15   13
5   0.20   15
6   0.40   14
7   0.25   15
8   0.50   9
9   0.15   17
10   0.30   13
11   0.20   10
12   0.15   15
13   0.40   18
14   0.45   19
15   0.15   15

Part a) Use the​ least-squares method to develop a singleregression equation with Time as the dependent variable and Tamp asthe independent variable. (Can you show me the step by step processusing PHSTAT on all answers)

part b) Predict the mean separation time for a tamp distance of0.45 inch.

part c) Plot the residuals versus the time order ofexperimentation. Are there any noticeable​ patterns?

part d) Compute the​ Durbin-Watson statistic. At the 0.05 levelof​ significance, is there evidence of positive autocorrelationamong the​ residuals?

Part E) Based on the results of​ (c) and​ (d), is there reasonto question the validity of the​ model?