DATA A repair workshop finds it is having a problem with a pressure gauge it uses. It decides to have it checked by a specialist firm. The following data was obtained. Reading of Gauge x (bar) 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 Correct reading y(bar) 0.96 1.33 1.75 2.14 2.58 2.97 3.38 3.75 Determine at the 5% level whether there is evidence to indicate a linear relationship between reading of x and correct readings y. Find a 95% confidence interval for β1 Find the correlation coefficient By what percentage is the sum of squares of deviations of y about the mean (SSyy) is reduced by using ŷ rather than y̅ as a predictor of
Theory and Design for Mechanical Measurements
Measurement is a term that refers to analyzing a manufactured component regarding the degree of accuracy for dimensions, tolerances, geometric profile, roundness, flatness, smoothness, etc. Measurement always involves comparing the manufactured component or the prototype with a standard specimen whose dimensions and other parameters are assumed to be perfect and do not undergo changes with respect to time.Precisely in mechanical engineering the branch that deals with the application of scientific principles for measurements is known as metrology. The domain of metrology in general deals with various measurements like mechanical, chemical, thermodynamic, physical, and biological measurements. In mechanical engineering, the measurements are limited to mechanical specific such as length, mass, surface profile, flatness, roundness, viscosity, heat transfer, etc.
Basic principles of engineering metrology
Metrology is described as the science of measurement, precision, and accuracy. In other words, it is a method of measurement based on units and predefined standards.
DATA
A repair workshop finds it is having a problem with a pressure gauge it uses. It decides to have it checked by a specialist firm. The following data was obtained.
|
Reading of Gauge x (bar) |
1.0 |
1.4 |
1.8 |
2.2 |
2.6 |
3.0 |
3.4 |
3.8 |
|
Correct reading y(bar) |
0.96 |
1.33 |
1.75 |
2.14 |
2.58 |
2.97 |
3.38 |
3.75 |
- Determine at the 5% level whether there is evidence to indicate a linear relationship between reading of x and correct readings y.
- Find a 95% confidence interval for β1
- Find the correlation coefficient
- By what percentage is the sum of squares of deviations of y about the mean (SSyy) is reduced by using ŷ rather than y̅ as a predictor of
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