In: Statistics and Probability
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
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 |