Question

When survey data indicated that a company needed to improve its​ package-sealing process, an experiment was conducted to determine the factors in the​ bag-sealing equipment that might be affecting the ease of opening the bags without tearing the inner liner of the bag. 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 the regression equation is the following. Complete parts​ (a) through​ (c).

ModifyingAbove Upper Y with caret Subscript iYiequals=0.79060.7906plus+0.46820.4682Xi​,

with

Summation from i equals 1 to n∑i=1nYiequals=14.7414.74​,

Summation from i equals 1 to n∑i=1nUpper Y Subscript i Superscript 2Y2iequals=40.320240.3202​,

and

Summation from i equals 1 to n∑i=1nXiYiequals=20.1720.17.

Bag	Plate gap (X)	Tear rating (Y)
1	-0.3	0.09
2	0.3	0.08
3	2.1	0.47
4	1.5	0.82
5	0	0.32
6	-0.3	0.36
7	-0.3	0.78
8	-0.3	1.93
9	0	0.23
10	-1.5	0.13
11	-1.5	0.12
12	2.4	3.96
13	-2.1	0.04
14	0	0.56
15	-3	0.01
16	-2.1	0.05
17	2.1	0.43
18	2.1	4.31
19	0.3	0.05

a. Determine the coefficient of​ determination, r2​,and interpret its meaning.

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

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

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

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

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

b. Determine the standard error of the estimate.

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

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

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

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

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

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

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

b. Determine the standard error of the estimate.

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

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

Answer 1

Excel > Data > Data Anlysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.5783542
R Square	0.33449358
Adjusted R Square	0.295346144
Standard Error	1.063379601
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9.661868187	9.661868187	8.54445681	0.009486453
Residual	17	19.22319497	1.130776175
Total	18	28.88506316
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	0.790573823	0.244008436	3.239944641	0.004815081	0.275761025	1.305386622	0.275761025	1.305386622
Plate gap (X)	0.468171072	0.160163056	2.923090284	0.009486453	0.130256562	0.806085583	0.130256562	0.806085583

a)

the coefficient of​ determination, r2 = 0.3345

It is the proportion of the variation in the tear rating that is explained by the variability in the plate

33.45% of the variation in the tear rating that is explained by the variability in the plate

b)

Standard error of the estimate, Se = 1.0634

c)

r^2 is nearer to 0.5 and Standard error is relatively large, so the model is fairly useful for predicting tear rating