2. At a hydrocarbon processing factory, process control involvesperiodic analysis of samples for a certain process qualityparameter. The analytic procedure currently used is costly and timeconsuming. A faster and more economical alternative procedure hasbeen proposed. However, the numbers for the quality parameter givenby the alternative procedure are somewhat different from thosegiven by the current procedure, not because of any inherent errorsbut because of changes in the nature of the chemical analysis.Management believes that if the numbers from the new procedure canbe used to forecast reliably the corresponding numbers from thecurrent procedure, switching to the new procedure would bereasonable and cost effective. The following data were obtained forthe quality parameter by analyzing samples using bothprocedures:
| Current (Y) | Proposed (X) | Current (Y) | Proposed (X) |
| 3.0 | 3.1 | 3.1 | 3.1 |
| 3.1 | 3.9 | 2.7 | 2.9 |
| 3.0 | 3.4 | 3.3 | 3.6 |
| 3.6 | 4.0 | 3.2 | 4.1 |
| 3.8 | 3.6 | 2.1 | 2.6 |
| 2.7 | 3.6 | 3.0 | 3.1 |
| 2.7 | 3.6 | 2.6 | 2.8 |
a. Use linear regression to find a relation to forecast Y, whichis the quality parameter from the current procedure, using thevalues from the proposed procedure, X.
b. Is there a strong relationship between Y and X? Explain.
