# Solution Library

# Testing Hypothesis Using Regression Model And R-Square Tests

**Question**

Using the **ustudy.sav** file, the following hypothesis will be tested:

H1: The likelihood of a faculty being in a public or a private university is predicted by the number of years since they got their doctorate and their salary.

Dependent variable**:**

- UNIV (type of university) = dependent binary variable (if the dependent variable has more than two levels, a multinomial logistic regression must be used instead of the binary one)

Independent variables**:**

- YRSPHD (years since PhD) = independent variable with ratio data
- SALARY (salary) = independent variable with ratio data

Note: Categorical variables (with nominal or ordinal data) can be included in the regression model. If such categorical predictors exist, they must be declared as *Categorical* in the SPSS *Logistic Regression* window. SPSS will dummy-code these variables automatically.

Procedure**:**

To test the predictive model, a binary logistic regression will be performed as follows:

- select
*ANALYZE / REGRESSION / BINARY LOGISTIC..*from the menu; - move UNIV in the
*Dependent*area and variables YRSPHD and SALARY in the*Covariates*area; make sure "Enter" is selected under*Method;* - click
*OK*.

**EXERCISE****.**Answer the following questions:

- What are the most important differences between linear multiple regression and binary/multinomial logistic regression?
- Is the regression model significant? Explain.
*(Check the chi-square df, and p of the model in the Omnibus Tests of Model Coefficients)* - What are the “R-square” values and how do you interpret it?
*(See the Model Summary section of the SPSS output.)* - Explain the difference between the Cox & Snell and the Nagelkerke R-square indicators. (see Hair & al.)
- What is the interpretation of the -2 Log likelihood value?
- Are the predictors statistically significant? Explain.
*(See the Variables in the Equation table.)* - Why are Wald tests used to answer #5 above and not t-tests like in multiple regression?

**Summary**

The question belongs to Statistics and it discusses about validating or testing a hypothesis using various tests such as regression model, R-square and multiple regression tests.

**Total Word Count 1099**

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