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Statistics_for_Data_Scientists (SDS) course assignments

The repository contains five tasks according to the following structure:

1- Logistic regression.

Assignment 1 was about fitting a logistic regression for the following:

- The effect of the ozone and cultivar on the infection

# Logistic regression model formulation:
p(x) = 1/(1+exp(beta0 + beta1*ozone + beta2*cultivar + beta3(cultivar*ozone)))

- The interaction between ozone and cultivar by comparing a full and reduced model

# Full model:
lgF <- glm(cbind(Infected, 1-Infected)~cultivar+ ozone+ cultivar:ozone, data = data, binomial)

# Reduced model:
lgR <- glm(cbind(Infected, 1-Infected)~cultivar+ ozone, data = data, binomial)

A brief explanation of the data:

Botrytis cinerea is a pathogen that can infect beans (Phaseolus vulgarus). One expects that the damage is more severe in plants that are weakened due to ozone gas. To investigate this, 20 days old plants of 3 cultivars (Strat, Pros, and Lit) are taken and given an ozone treatment with concentrations 0, 120, 180, or 270 ppm. For each concentration, 30 plants of each cultivar were used. Subsequently, each plant was inoculated with botrytis and after a few days, it was observed if a plant was infected or not. The data can be found in the file botrytis.csv.

2- Regularized regression.

The goal of Assignment 2 is to predict ash content from spectra by creating a model with a good fit using cross-validation, regularized regression, and lasso regression techniques.

A brief explanation of the dataset:

The dataset in this exercise consists of ash content (in percentages) and fluorescence spectra from 324.5 to 560.0 nm of 265 samples of sugar. The Ash content of refined granulated sugar must not exceed 0.015% by most standards. Ash content can be reduced by maintaining proper filtration, sufficient washing during centrifugation of the sugar, and proper handling of the sugar during drying and screening. The data are in the file SugarData.Rdata.

3- Linear mixed models.

In Assignment 3, we explored mixed models through using ANOVA and REML.

A brief explanation of the experiment:

experiment to investigate the influence of two levels of feed ratio on the growth of
animals. It is also investigated whether the feed ratio has a similar effect for males and females. In setting the experiment, 24 animals were selected from 12 representative litters. Pairs of 6 males and 6 females were randomly selected from the representatives and two feed ration levels are randomly assigned to the pairs making the design a split plot. The growth per animal over a fixed period of time is predicted using the feed ratio and sex level variables. Since the representatives are from the same parent, this introduces dependence in the paired variable and thus the choice for mixed models. Summary of data shows the mean growth of animal is 31.45.

4- General additive models (GAMs).

Assignment4 focused on applying generalized additive models (GAMs) for predicting grain number in a specific maize hybrid. Our analysis focused on a single maize hybrid grown in 25 different environments(observations) under 14 different environmental characterizations(variables).

5- Trre-based methods.

In Assignment 5, we predicted patients with the liver disease either positive or negative using tree-based methods such as Random Forest, Bagging, and Boosting algorithms with different settings and hyperparameters to investigate the different accuracy in each model, Also, the specificity and sensitivity to measure the performance of all classification models. Moreover, logistic regression was used to predict positive cases of liver disease, and the comparison was applied with the tree-based methods. The provided datasets contain 400 patient profiles which include the gender, age, and other eight enzyme ratios (10 observations in total).