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

Grouped Data For calculating mode from a frequency distribution, the following formula   Mode = L mo +  x W where,


You were recently hired by E&T Boats, Inc. to assist the company with its financial planning and to evaluate the company's performance.  E&T Boats, Inc. builds and sells boats to o

(1) What values can the response variable Y take in logistic regression, and hence what statistical distribution does Y follow? The response variable can take the value of either



for this proportion, use the +-2 rule of thumb to determine the 95 percent confidence interval. when asked if they are satisfied with their financial situation, .29 said "very sat

Stratified Sampling Stratified Sampling is generally used when the population is heterogeneous. In this case, the population is first subdivided into several parts (or s

Convenience Sampling It means a convenient sample is obtained by selecting convents units from the universe. Convenient sample is also known as chunk. It   means a fraction of