Regression and Correlation of Data
Other forms with single input or regressor:
1 = a + bx y
ln y = a + bx
y = a + bx 3
f1( y) = a + b f2 (x)
Method: 1. Convert the equation to simple linear form by setting new variable(s). 2. Calculate the new variable(s)
Statistical Inferences for Variance
Objectives:
Learn to compare variance of a sample with variance of a population Learn to compare variance of a sample with variance of another sample Introduce chi-squared distribution chi squared Introduce F-distribut
Statistical Inference for the Mean: t-test
Comparison of paired samples: - Interfering factors in the comparison of two sample means using unpaired samples may inflate the pooled estimate of variance of test results. - It is possible to pair the measureme
Statistical Inference for the Mean: t-test
Comparison of sample means using unpaired samples: - We have samples for each of two conditions. We provide an answer for "Are the two sample means significantly different from Are each other, or could both plaus
Note 7
Statistical Inference for the Mean: t-test
When variance is estimated from a sample, t-distribution applies. T-Distribution: a distribution related to normal distribution but taking into account the number of degrees of freedom. freedom Symmetrical
Normal Distribution
Objectives: (Chapter 7, DeCoursey)
- To define the Normal distribution, its shape, and its probability function p y - To define the variable Z, which represents the number of standard deviations between any y point x and the mean . - T
One way One-way Analysis of Variance
ANOVA Analysis of Variance is used with quantitative and qualitative data to find whether each input has significant effect on the system's response.
Estimates of variance are often called "mean mean squares"
s =
2
Regression and Correlation of Data
- Apply the least squares method for fitting data with linear regression - Methods of regression are used to summarize sets of data in useful form. The values of the data have already been recorded, and as such, are fixe
Probability Distributions, Discrete Random Variables
Objectives: (Chapter 5, DeCoursey)
- To define a probability function, cumulative p probability, p y probability distribution function y and cumulative distribution functions. - To define expectation an
Probability Distributions, Continuous Variables
Objectives: (Chapter 6, DeCoursey)
- To establish the difference between probability distribution for discrete and continuous variables. - To learn how to calculate the probability that a random variable, X,
Regression and Correlation of Data
Objective:
Fit a polynomial with the Least Squares Method
Regression and Correlation of Data
Fitting the polynomial with the least squares approach
Pn ( x) = a 0 + a1 x + a 2 x 2 + . + a n x n
Least squares method can
Normal Distribution
Objectives: (Chapter 7, DeCoursey)
- To define the Normal distribution, its shape, and its probability function p y - To define the variable Z, which represents the number of standard deviations between any y point x and the mean . - T
Introduction to Design of Experiments
Professional engineers are very frequently responsible for devising d i i experiments t answer practical problems. Th i t to ti l bl There are well-tried methods for planning experiments that will p provide the maximu
To calculate the number of combinations for n distinguishable items: Three laboratories to be cleaned: Biosorption, Pilot Plant and Fermentation. How many different combinations of cleaning the three laboratories? n=3, r=2
1st B B P P F F 2nd P F B F B P
Descriptive Statistics
Objectives: (Chapter 3, Decoursey)
- To understand the definition of , median, variance, standard deviation, mean absolute deviation and coefficient variation and calculate these quantities. - To calculate some of these quantities u
Regression and Correlation of Data
Correlation: Correlation is a measure of the association between random variables, say X and Y. No assumption that one of these variables is known without error. Assume that X and Y are related linearly, so the usual cor
Confidence level: An alternative representation of level of significance. - normal distribution applies applies. - level of significance (e.g. 5% in two tails) determines the rejection region, which means - in the rejection region sample means are far eno
Basic Probability
Permutations and Combinations:
- Combinations:
- The number of different packages of data taken r at time from a data set containing n items The order of items is items. inconsequential. The number of taken r at a time (r n) is written n
Basic Probability
(Chapter 2, W.J.Decoursey, 2003)
Basic Probability
Probability:
A measure of the likelihood that a particular event will occur. e.g. If we are certain that an event will occur, its probability is 1 or 100%. If it certainly will not occur