Sta3701 Assignment 4 Solutions 2023 Unisa Applied Statistics

STA3701
ASSIGNMENT 4
SOLUTIONS 2023
Unique number: *******

DUE DATE: 21SEPTEMBER 2023


APPLIED STATISTICS -
STA3701

, ASSIGNMENT 04
Unique Nr.: 859766
Due date: 18 September 2023




Instructions
1. Do not PLAGIARISE. Students suspected of plagiarism will be subjected to
disciplinary processes.
2. Use R to answer all the questions. Present or attach R outputs. Label all the
figures and tables.




1.1 Define analysis of variance (ANOVA): ANOVA is a statistical technique used to
analyze and compare the means of two or more groups or treatments to
determine if there are significant differences among them. It assesses
whether the variability between group means is greater than the variability
within the groups.
1.2 How is ANOVA different from regression analysis? ANOVA and regression
analysis are both used to analyze relationships between variables, but they
differ in their primary objectives:
• ANOVA assesses differences in means among groups or treatments.
• Regression analysis explores the relationship between a dependent variable
and one or more independent variables, aiming to predict or explain variations
in the dependent variable.
1.3 Explain the difference between one-factor (one-way) ANOVA and two-
factor (two-way) ANOVA:

, • One-factor (one-way) ANOVA examines the impact of a single categorical
independent variable on a continuous dependent variable. It tests for
differences in means among two or more groups.
• Two-factor (two-way) ANOVA extends the analysis to two independent
variables (factors) to assess their main effects and interaction effect on the
dependent variable. It allows for the study of how two factors jointly influence
the outcome.
Explanation:
let's provide a more detailed explanation for each part of the questions:
1.1 Define analysis of variance (ANOVA):
ANOVA is a statistical method used to compare the means of two or more groups or
treatments to determine if there are significant differences among them. It does this
by partitioning the total variance in the data into two components: variance between
groups and variance within groups. If the variance between groups is significantly
greater than the variance within groups, ANOVA indicates that at least one group
mean is different from the others.
1.2 How is ANOVA different from regression analysis:
ANOVA focuses on comparing means among groups or treatments to assess
differences or effects, typically in a categorical predictor variable.
Regression analysis, on the other hand, explores the relationship between a
dependent variable and one or more independent variables, aiming to predict or
explain variations in the dependent variable. It is used for continuous predictor
variables.
1.3 Explain the difference between one-factor (one-way) ANOVA and two-factor
(two-way) ANOVA:
One-factor (one-way) ANOVA: It examines the effect of a single categorical
independent variable (factor) on a continuous dependent variable. It assesses
differences in means among multiple groups or levels of the factor.
Two-factor (two-way) ANOVA: It extends the analysis to two independent variables
(factors), allowing for the study of their main effects and the interaction effect on the
dependent variable. It is suitable when you want to analyze how two factors jointly
influence the outcome.


1.4.1 What is the treatment variable in this study? The treatment variable in this
study is the type of calcium channel blocker used for hypertension treatment. It has
three levels: lercanidipine, felodipine, and nifedipine.
1.4.2 What is the response variable in this study? The response variable in this
study is the change in systolic blood pressure. It measures how much the systolic
blood pressure has changed in each patient after four weeks of treatment.