Question

MBA 5008 Quantitative Analysis The question presented to me which I dont fully understand and requesting assitance in answering.

When developing a simple regression model one utilizes a method to predict a linear relationship between a dependent variable and an independent variable.

However, there may be more than one independent variable that affect the dependent variable. In this case we utilize the multiple regression method.

1. Describe the objective in using simple and or multiple regression models.

2. What does the ANOVA (analysis of variance) table demonstrate?

3. Define the coefficient of determination (r-square) and interpret its results (i.e. weak or strong relationship).

4. How do we determine whether our model determines a significant relationship between our variables? Evaluate at least two methods to arrive at your conclusions.

5. Describe the statistical inferences one can make utilizing the results of a regression model.

Answer 1

1. The objective of multiple regression is to understand more about the relationship between several independent or predictor variables and a dependent variable. Simple regression is used when we are very sure about the fact that the dependent variable is mostly dependent on only one independent variable but, when we are not sure of this fact then we also want to utilize the information contained in other independent variables, then we use multiple linear regression model.

2. Analysis of Variance (ANOVA) table consists of calculations which provide the information about variability of information contained in different variables. It is used to compare the amount of information contained in different variables. It is also used to test the significance of different variables.

3. The coefficient of determination (also called R²) is the proportion of the variance in the dependent variable that is predictable from the independent variable. In simple terms, it represents the amount of the variance contained in the dependent variables are being explained by independent variables. For example of R² of 0.8 says that model is able to explain 80% of the variance that is there in dependent variable.

4. As told above, R² is one of the criteria which determined whether there is a significant relationship between our variables in the model. A higher value shows a better strength of the model.

F-score in the anova table or adjusted R-Square can also be other methods to evaluate the significance of relationship.

5. You can have a t-test done for every individual coefficient of the different variables in linear regression. That will give you an idea about their individual significance in the model.

You can have a confidence interval created for your output values using the confidence interval of your coefficients predicted in linear regression.

You can check whether errors are normally distributed on the training set or not.

You can check whther variance of errors are constant everywhere or not using the residual plot or Normal Q-Q plot.