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
Question: A car was machine washes each car in 5 minutes exactly. It has been estimated that customers will arrive according to a Poisson distribution at an average of 8 per hour.

Examples of grouped, simple and frequency distribution data


discuss the mathematical test of adequacy of index number of formulae. prove algebraically that the laspeyre, paasche and fisher price index formulae satisfies this test. What is

(1) Assume we categorize voters in a city as havingless educationand those havingmoreeducation. Those with less education have less than a college degree; those with more education

what is the independent variable in how energetic do people feel after drinking different types of soft drints?

Analysis of Variance for the data: Draw a random sample of size 25 from the following data : (a) With Replacement and   (b) Without Replacement and obtain Mean and Varia

Statistical Keys To do statistical operations we must first set the calculator on SD mode [SD stands for "standard deviation" which is the usual st

how to compute reliability coefficient for extracted factors in factor analysis?

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