In: Statistics and Probability
Please use mintab
The strength of a part was monitored as a function of temperature within a process. Generate a Scatter Plot, determine the value of the coefficient of correlation, generate a Fitted Line Plot, generate a Residual Plot, and estimate the percentage of variability in strength as a function of temperature. Note: Data divided into six columns for visual display. Your analysis should have a single Temp column and a single Strength column.
| 
 Temp  | 
 Strength  | 
 Temp  | 
 Strength  | 
 Temp  | 
 Strength  | 
| 
 140.6  | 
 7.38  | 
 140.5  | 
 6.95  | 
 142.1  | 
 3.67  | 
| 
 140.9  | 
 6.65  | 
 139.7  | 
 8.58  | 
 141.1  | 
 6.58  | 
| 
 141.0  | 
 6.43  | 
 140.6  | 
 7.17  | 
 140.6  | 
 7.42  | 
| 
 140.8  | 
 6.85  | 
 140.1  | 
 8.55  | 
 140.5  | 
 7.53  | 
| 
 141.6  | 
 5.08  | 
 141.1  | 
 6.23  | 
 141.2  | 
 6.28  | 
| 
 142.0  | 
 3.80  | 
 140.9  | 
 6.27  | 
 142.2  | 
 3.46  | 
| 
 141.6  | 
 4.93  | 
 140.6  | 
 7.54  | 
 140.0  | 
 8.67  | 
| 
 140.6  | 
 7.12  | 
 140.2  | 
 8.27  | 
 141.7  | 
 4.42  | 
| 
 141.6  | 
 4.74  | 
 139.9  | 
 8.85  | 
 141.5  | 
 4.25  | 
| 
 140.2  | 
 8.70  | 
 140.2  | 
 7.43  | 
 140.7  | 
 7.06  | 
Using Excel, go to Insert Scatter Plot.

Using Excel, go to Data, select Data Analysis, choose Regression. Put Temperature in X input range and Strength in Y input range. Tick Residual Plot and Line Fit Plot.
| SUMMARY OUTPUT | |||||
| Regression Statistics | |||||
| Multiple R | 0.977 | ||||
| R Square | 0.955 | ||||
| Adjusted R Square | 0.953 | ||||
| Standard Error | 0.347 | ||||
| Observations | 30 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 71.054 | 71.054 | 588.593 | 0.000 | 
| Residual | 28 | 3.380 | 0.121 | ||
| Total | 29 | 74.434 | |||
| Coefficients | Standard Error | t Stat | P-value | ||
| Intercept | 333.986 | 13.496 | 24.747 | 0.000 | |
| Temperature | -2.324 | 0.096 | -24.261 | 0.000 | 


Correlation coefficient (Multiple R) = 0.977
Percentage of variability in strength as a function of temperature (R-square) = 0.955 = 95.5%