b. In your own words, explain what multiple regression and structural equation m

Question

b. In your own words, explain what multiple regression and structural equation model have in common. Also explain main differences between the two (5 points) c. Multiple regression analysis is concemed with the prediction of a dependent variable Y by a set of independent variables A's. Provide the formula for the multiple regression with k independent variables in a population parameter form. What are the interpretations of the unstandardied intercept and regression (slope) coefficients in the model? (5 points)

Explanation / Answer

Part-B

Multiple regression tries to related one variable called dependent variable to be explained by one or more variables called explanatory variables. In a similar fashion, SEM explain the variables from one or more of the other explanatory variables. So the two procedures are similar in the sense that they have dependent and independent variables.

However, there is a potential main difference which is that in multiple regression we have only one dependent variable to be explained by other variables and this dependent variable can not be used to explain other. On the other hand in SEM there could be more than one dependent variables and they can also explain each other and can play the role of independent as well as independent variables.

Part-C

Multiple regression analysis model is as follows:

Yi= 0 + 1 X1+ 2 X2+ …… k-1 Xk-1 + k Xk + i

Where i, i=1,2,…n are errors in predictor which are normal distributed and have zero mean and fixed variance. Also , error are independent.

Intercept is the mean value of dependent variable when predictors are held at zero level.

Slope of Xj,, j=1,2,…k is the average change in Y corresponding to unit increase in Xj, ceteris peribus.

Part-d

Unstandardized regression coefficient is proved as follows:

Suppose all other variables are held fixed except Xj

Than

Y=j*Xj, as difference in intercept is zero becaue it is constant and difference inn other predictors is zero as they are fixed.

So this implies the definition of coefficient of Xj

Problem-3

Part-a

Latent variables are the variables which are not measured directly but are explained by other observed variables. The observed variables are those whose values can be taken practically and define latent variables.

Exploratory factor analysis is used to explore factor and confirmatory factor analysis confirms whether the factors created are really useful or exists. Causal infercen can be made from CFA but not from EFA because CFA confirsm the relationships and hence if one cause other that could be seen in CFA

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