Statistics Lecture Notes: Review of Correlation and Regression Analysis with Examples, Exercises of Electronic Measurement and Instrumentation

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M E 345 Professor John M. Cimbala Lecture 08

Today, we will :

 Do a review example problem – t PDF and chi-squared PDF  Review the pdf module: Correlation and Trends and do some example problems  Review the pdf module: Regression Analysis and do some example problems

Example: Estimating population mean and population standard deviation Given : 20 ball bearings are pulled from the assembly line, and their diameters are measured. The sample mean is 2.56 mm and the sample standard deviation is 0.240 mm. ( a ) To do : Estimate the population mean and its confidence interval for 98% confidence level.

( b ) To do : Estimate the population standard deviation and its confidence interval for 98% confidence level.

Solution :

Example: Linear correlation coefficient Given : Matt measures both the shoe size and the weight of 18 football players. He performs a linear regression analysis of shoe size ( y variable) as a function of weight ( x variable). He calculates r (^) xy = 0.582.

To do : To what confidence level can Matt state that a football player’s shoe size is correlated with his weight?

Solution :

Example: Linear correlation coefficient Given : Several measurements are taken in a wind tunnel of pressure difference as a function of distance normal to the direction of flow over a body.

Data point x (mm)  P (kPa) 1 0 0. 2 2.0 0. 3 4.0 0. 4 6.0 0. 5 8.0 0. 6 10.0 0. 7 15.0 0. 8 20.0 0.

( a ) To do : Calculate the linear correlation coefficient

( b ) To do : To what confidence level can we state that there is a trend in the data?

Solution :

Example: Regression Analysis Given : The same pressure vs. distance measurements of the previous problem.

To do : Perform a linear regression analysis – plot the best-fit straight line and compare the fitted curve to the data points.

Solution :

See Excel spreadsheet – I will show in class how to do the regression analysis in Excel.