Question

1. What is the difference between simple linear regression and multiple linear regression?

2. What is the difference between multiple linear regression and logistic regression?

3. Why should you use adjusted R-squared to choose between models instead of R- squared?

4. Use SPSS to:

Height (Xi)	Diameter (Yi)
70	8.3
72	10.5
75	11.0
76	11.4
85	12.9
78	14.0
77	16.3
80	18.0

1. Create a scatterplot of the data above. Without conducting a statistical test, does it look like there is a linear relationship between tree height and diameter?

2. Does the relationship look positive or negative? Please fully explain all of your answers.

Answer 1

1)

In simple linaer regression we only have one predictor that is, the X variable But in Multiple linaer reression we have one or more than one predictor to predict the response variable. We can say that SLR is a particular case of MLR.

2)

The essential difference between these two is that Logistic regression is used when the dependent variable is binary in nature. In contrast, Multiple linear regression is used when the dependent variable is continuous and nature of the regression line is linear. plus, the MLRM use oridinary least square approach to find coefficients of predictor and Logistic regression use maximum likelihood method to find coefficients of predictors.

3)

R2 value always increases as the number of predictors because the SSR value always increase as the number of predictors increase.

we can see from the above formula that adjusted R2 includes there respective degree of freedom and from that we can see that p the number os predictor is inversly proportional to adjusted R2 value. So, when the increase due to adding a new predictor is not significant in the SSR value the adjusted R2 value decreases due to penalty of number of predictor. So, we know that the particular vartiable is not explaning model significantly. That's why we prefer adjusted R2 over R2.

4)

we can see from the below scatter plotthat almost all the points are in a line that implies there the relationship is linear as the height of the tree increase the diameter of the tree also increases with it. So, there is a positive relationship between height and diameter