Simple linear regression, Applied Statistics

Simple Linear Regression

 

While correlation analysis determines the degree to which the variables are related, regression analysis develops the relationship between the variables.

Thus coefficient of correlation indicates the strength of a linear relationship. And here we compute the linear model that best fits the relationship. Once again, we reiterate the importance of using qualitative analysis to arrive at a cause and effect relationship before computing the model. 

Regression analysis is based on the relationship between two or more variables. The known variable is the independent variable and the variable we are trying to predict is the dependent variable. An inverse relationship exists between the variables.

If X represents the cause and Y, the effect, we are searching for

                    1885_simple linear regression.png  = E(Y|X = x) = A + Bx,

i.e., if X takes on the value x, we would expect Y to assume A + Bx.

Since it is (usually) impossible to obtain all possible pairs (X, Y), we need to estimate the model using a sample. The approximate model is given by

                   E (Y|X = x) = a + bx

In this case, a is an estimate of A and b is an estimate of B.

We may rewrite the population regression line and the sample regression lines as,

                   y = A + Bx + ex

and

                   y = a + bx + ex

Where ex and ex are random variables with mean 0.

Posted Date: 9/15/2012 5:02:06 AM | Location : United States







Related Discussions:- Simple linear regression, Assignment Help, Ask Question on Simple linear regression, Get Answer, Expert's Help, Simple linear regression Discussions

Write discussion on Simple linear regression
Your posts are moderated
Related Questions
The data in the data frame asset are from Myers (1990), \Classical and Modern Regression with Applications (Second Edition)," Duxbury. The response y here is rm return on assets f

The Quality Manager of a battery manufacturing plant reviewed the warranty records within his department and found that 4% of the low maintenance batteries produced at the plant ov


Do people of different age groups differ in their response to e-mail messages? A survey by the Cent of the Digital Future of the University of Southern California reported that 70.

You are currently working with a supplier who is producing a shaft whose diameter specification is 6.00 ± .003 inches.  Currently, the process is yielding shafts wit

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

give me question on mean is the aimplest average to understand and easy to compute

For many decades, there has been considerable attention paid to identifying various factors that help to reduce the number of fatalities on Australian roads. In 1964 Victoria and S

i am new to stata and i am trying to figure out how to calculate expected growth of sales tax revenue as well as average growth rate of sales tax revenue in stata. I have a dataset

a. How can break-even analysis be used in selecting a new plant site? b. What are potential advantages and disadvantage of locating a production facility in foreign country i