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Linear regression in statistics

LINEAR REGRESSION ANALYSIS 

BY INIOBONG EMMANUEL 08138223438

Introduction What is linear regression Application of linear regression. Criteria for linear regression test.

Regression is concerned with predicting or estimating the value of variable from another variable(s). The simplest form of regression is the linear regression.

What is a linear regression Linear regression is concerned with estimating value of a dependent variable (continous) from an independent variable (continuous). In other words, both variables are interval or scale. The following are vital in a linear regression analysis;

1. The graph of linear regression plots a slopy line between the x- axis and the y- axis. This line is also called line of prediction. Its a predicting line because for every given value of the independent (predictor) variable there is a corresponding value of the dependent variable.

2. This line plots the independent variable on the x-axis and the dependent variable on the y-axis. Both variables are of a continuous scale.

3. The equation that estimates the value of the dependent variable with the aid of an independent variable is given by

                   y =c + mx

Where y is the value of the dependent variable estimated or predicted with independent variable x.

m is the slope of the line of dependency.

c is a constant.

4. This scenario best describes a linear regression.

5. The dependent variable or variable to be predicted is also known as endogenous variables.

6. The independent variable or variable used for predicting the value of the dependent variable is also called predictor or exogenous variable.

Applications of linear regression

1. I am a farmer i want to estimate the amount of my crop yield with the amount of rainfall.

Can you see? One variable is the cause for another. Regression is useful in a casual relationship.

The dependent variable (amount of crop yield) is measured and its of a continuous value. The independent variable (amount of rainfall) is measured and its of a continuous value. This process is successful through data collection of previous amount of rainfall crop yields respectively.

2. I am a teacher, I want to predict the score of students in math when I check for scores in quantitative reasoning. The dependent variable is maths. It is predicted using an independent variable quantitative reasoning.

Criterias for linear regression test.

1. Correlation test: test for the type of relationship between variables. It is measured by a correlation coefficient.

Coefficient of correlation spans across two points namely ; -1 to 1 indicating positive or negative relationship.

If the coefficient is close to +1 the relationship is strongly positive we can depend on our result. If the relationship is close to -1 it is strongly negative, hence we can trust our result to be perfect.

2. Normality test. This test indicates if there is a line of symmetry from the distribution and thus makes linear regression test valid.

To test for normality , smirnov test is used for continuous variables. To run a 1- sample kologorov - Smirnov,

Goto analyze Non-paracontinous level test Legacy dialogue 1- sample k.s

If the significance level is less than 0.05 variable does not approximate a normal distribution I.e significance level< 0.05 = not a normal distribution vice versa.

Normality test is a criteria for linear regression test. variables must be normal to make the result valid.

References linear regression in spss retrieved at statisticsolution.com

Gupta, S.C. (2012). Fundamentals of statistics:revised edition, Hamalaya publishing House.

HOW TO PERFORM LINEAR REGRESSION Follow the following steps to conduct a linear regression test. Goto Analyze Click on regression >> linear Drag the dependent variable to the dependent box. Drag the independent variable to the independent list box.

Click on plots select the ZRESID to Y box: this represents the dependent variable. And ZPRED to the X box. This represents our independent variable. Click on OK.

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