When survey data indicated that a company needed to improve its​package-sealing process, an experiment was conducted to determinethe factors in the​ bag-sealing equipment that might be affectingthe ease of opening the bags without tearing the inner liner of thebag. Data were collected on 19 bags and the plate gap on the​bag-sealing equipment was used to predict the tear rating of a bag.The results are displayed in the accompanying table and theregression equation is the following. Complete parts​ (a) through​(c).

ModifyingAbove Upper Y with caret SubscriptiYi=0.75380.7538+0.5302Xi​,

with Summation from i equals 1 ton∑i=1nYi=14.6414.64​,

Summation from i equals 1 to n∑i=1nUpper Y Subscript iSuperscript 2Y2i=38.6848​,

and Summation from i equals 1 ton∑i=1nXiYi=19.73.

Bag   Plate gap (X)  Tearrating (Y)
1   -0.3   0.03
2   -0.30   0.06
3   1.50   0.41
4   1.50   0.82
5   -0.30   0.36
6   0.00   0.37
7   0.30   0.75
8   0.00   1.98
9   0.00   0.24
10   -1.80   0.17
11   -1.80   0.13
12   2.40   3.72
13   -1.80   0.03
14   0.00   0.52
15   -2.70   0.01
16   -1.80   0.13
17   1.80   0.44
18   2.10   4.06
19   0.30   0.07

a. Determine the coefficient of​ determination, r2​, andinterpret its meaning. (Fill in the Blank)

r2 = ___? ​(Round to four decimal places as​needed.)

What is the meaning of the coefficient of​determination? (Choose Below)

A. It measures the variability in the actual plate gap from thepredicted plate gap.

B. It measures the variability in the actual tear rating fromthe predicted tear rating.

C. It is the proportion of the variation in the plate gap thatis explained by the variability in the tear rating.

D. It is the proportion of the variation in the tear rating thatis explained by the variability in the plate gap.

b. Determine the standard error of theestimate.

SYX = ___? ​(Round to four decimal places as​needed.)

c. How useful do you think this regression model is forpredicting the tear rating based on the plate gap in the​bag-sealing equipment? (Choose Below)

Since the value of r2 is (fairly close to 0, fairlyclose to 1, fairly close to 0.5, equal to 1, equal to 0)and the value of SYX is (relatively large, relativelysmall) the regression model is (not very useful,fairly useful) for predicting the tear rating.