### Homework 1: 2-way ANOVA

## Problem Statement:

In this SPSS homework, we aim to explore the relationships between gender, job classification, and their interaction effect on employees' salaries. The null and alternative hypotheses are formulated as follows:

**Solution
**

**Null Hypotheses:
**

- There is no difference in the mean of salary between male and female employees.
- There is no difference in the mean of salary among clerical, technical, and professional employees.
- There is no interaction effect between gender and job classification.

**Alternative Hypotheses:
**

- There is a difference in the mean of salary between male and female employees.
- There is a difference in the mean of salary among clerical, technical, and professional employees.
- There is no interaction effect between gender and job classification.

We'll analyze the data through statistical tests and ANOVA to determine if these hypotheses hold.

**Statistical Analysis and Interpretation:
**

**1. Levene's Test of Equality of Error Variances:
**

Levene's test examines whether the error variances of the dependent variable (SALARY) are equal across different groups. The results indicate that the error variances are the same across the groups, ensuring a valid basis for further analysis.

**2. Tests of Between-Subjects Effects:
**

This section displays the results of the 2-way ANOVA, which evaluates the effects of gender and job classification on salary. The key findings are as follows:

**Corrected Model:**The model has been adjusted and has an R-squared value of 0.471.**Intercept:**The intercept shows a significant effect on salary (p < 0.001).**SEX:**Gender has no significant impact on salary (p = 0.815).**CLASSIFY:**Job classification does not significantly affect salary (p = 0.209).**SEX * CLASSIFY:**The interaction effect between gender and job classification is not significant (p = 0.929).

In conclusion, the p-values for gender, job classification, and interaction effect are all greater than the significance level (0.056). Therefore, we fail to reject the null hypotheses, indicating no significant differences in salary between gender, job classification, and their interaction.

## Homework 2: Regression Analysis

### Problem Statement:

For this homework, we are examining the relationship between BMI and dining out frequency, while adjusting for gender, age, and race/ethnicity. The results of the regression analysis are presented as follows:

- The table provides parameter estimates for the various factors in the model, including gender, age, race/ethnicity, and dining out frequency.
- Significant interaction effects were observed between dining out frequency and both gender and race/ethnicity.
- The main effects of gender and dining out frequency significantly impact BMI after adjusting for other variables.

In the final part, a BMI prediction for a specific scenario is calculated.

## Homework 3: One-Way ANOVA

### Problem Statement:

In this homework, we investigate the average health scores among single, married, and divorced individuals. The null and alternative hypotheses are as follows:

**Null Hypothesis:**There is no difference in the average health score among single, married, and divorced people.**Alternative Hypothesis:**There is a difference in the average health score for at least one pair among single, married, and divorced people.

The analysis includes descriptives, a test of homogeneity of variances, and the ANOVA itself. Key findings are:

**Descriptives:**The summary statistics show the mean, standard deviation, and confidence intervals for each group (single, married, divorced).**Test of Homogeneity of Variances:**The variance of health scores among the three groups is found to be the same, meeting the homogeneity of variance assumption.**ANOVA:**The p-value for the ANOVA test is 0.823, indicating that we do not reject the null hypothesis. Therefore, there is no significant difference in the average health scores among the three groups.

In summary, the analysis suggests that there is no significant difference in health scores between single, married, and divorced individuals.