Question

In: Statistics and Probability

The effect of sealer plate temperature (X1) and sealer plate clearance (X2) in a soap wrapping...

The effect of sealer plate temperature (X1) and sealer plate clearance (X2) in a soap wrapping machine affects the percentage of wrapped bars (Y) which pass inspection. Obtain the residuals and draw a box plot of the residuals. Also prepare a normal probability plot. Interpret the plots and summarize your findings.

X1   X2   Y
190   130   35
176   174   81.7
205   134   42.5
210   191   98.3
230   165   52.7
192   194   82
220   143   34.5
235   186   95.4
240   139   56.7
230   188   84.4
200   175   94.3
218   156   44.3
220   190   83.3
210   178   91.4
208   132   43.5
225   148   51.7

Solutions

Expert Solution

Analysis:

the box plot indicates that there are no outliers for the residuals. tHE range of residuals is (15--15) = 30. The median value is one indicating that 50% of the residuals are less than 1

An S shape is formed in the normal probability plot. This indicates that the assumption of normality of residuals is followed.

process:

data -> Data Analytics -> regression

dependent variable -> Y

independent variables -> X1 and X2

output:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.897984626
R Square 0.806376388
Adjusted R Square 0.77658814
Standard Error 11.20467409
Observations 16
ANOVA
df SS MS F Significance F
Regression 2 6797.063 3398.531 27.07029 2.32E-05
Residual 13 1632.081 125.5447
Total 15 8429.144
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -67.8843597 40.58652 -1.67258 0.118289 -155.566 19.79749 -155.566 19.79749
X1 -0.064189113 0.163914 -0.3916 0.701696 -0.4183 0.289926 -0.4183 0.289926
X2 0.906088617 0.123371 7.344429 5.63E-06 0.639562 1.172615 0.639562 1.172615
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 37.71122898 -2.71123
2 78.47777573 3.222224
3 40.37274675 2.127253
4 91.69885237 6.601148
5 66.85676605 -14.1568
6 95.57252226 -13.5725
7 47.5647076 -13.0647
8 85.56368144 9.836319
9 42.65657086 14.04343
10 87.69680424 -3.2968
11 77.84332562 16.45667
12 59.47223785 -15.1722
13 90.15087261 -6.85087
14 79.91970034 11.4803
15 38.36800217 5.131998
16 51.77420512 -0.07421

orchestra answered 3 years ago
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