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Multiple linear regression

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  MULTIPLE LINEAR REGRESSION   INTRODUCTION: It is used to estimate the relationship between two or more independent variables and one dependent variable. The independent variables can be continuous ( or) categorical ( dummy coded as appropriate). You can use MULTIPLE LINEAR REGRESSION ; how strong the relationship is between two ( or) more  independent variables and one dependent variable  the value of dependent variable at certain value of the independent variables . ASSUMPTIONS: It is also same assumptions as simple linear regression Homoscedasticity : the size of the error in our prediction doesn’t change significantly across the values of independent variable. Independence of observations : the observations in the dataset were collected using statistically valid methods and there are no hidden relationship among variables. In multiple LINEAR REGRESSION, it is possible that some of the independent variable are actually correlated with one another , so it is important to check the
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WHAT IS RELIABILITY IN STATISTICS

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  What is reliability in statistics with example in SPSS      What is reliability ? Extent to which results are consistent Validity is the extent to which the instrument measures what it claims to measure. A good measurement instrument is both reliable and valid. Reliability is a prerequisite for validity.      Ways to measure Reliability: Test – Retest Parallel forms Split-half method Internal consistency      Interpreting Test – Retest and Parallel Forms                  Reliability:  Measured with correlation coefficient between halves or between tests. Generally an range of 7-8 is considered good reliability, but it depends on what else is available.      Split – half Method: A method of determining the reliability of a test by dividing the whole test into two halves and scoring the two halves separately.      Inter – rater reliability: It as the name indicates relates to the measure of sets of results obtained by different assessors using same methods. Benefits and importance of
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WEIGHTED LEAST SQUARES METHOD

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WEIGHTED LEAST SQUARES WITH EXAMPLES   what is weighted least square: Weighted least square regression , also known as weighted linear regression , is a generalization of ordinary least squares and linear regression in which knowledge of the variances of observations is incorporated into the regression. It’s an extension of ordinary least squares regression. Non – negative constants ( weights) are  attached to data points . It’s handle cases where data quality varies  .i.e., one of the common assumptions underlying most process modelling methods , including linear and non linear least square regression ,is that each data  point provides  equally precise information about the deterministic part of the total process variation. In weighted fit , less weight is given to the less precise measurements and more weight to more precise measurements when estimating the unknown parameters in the  model. Using weights that are inversely proportional to the variance at each level of the  explanator
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