Alzheimer’s Disease (AD) is a serious disease which is frequently in the news nowadays. Almost 1/3 of elderly people have this disease. Some biological factors are found to be associated with it, such as gender, age and education level. The governments all over the world have paid a large amount of money to solve this problem, but the result is not as good as people expected. AD cannot be cured at this time. To find as soon as possible whether a person has AD is the best way to control AD. My goal in this thesis is to describe some models to help discover the presence of AD in clinical trials. The original data is collected by OASIS (Open Access Series of Imaging Studies). We have about 400 subjects in this research. Due to missing value and data quality, only 235 subjects have provided the entire information. I will consider these 235 subjects in this thesis, and 100 of them have AD. To analyze the brain image data of AD patients, the high dimension of the image is the most important problem that should be solved. Principal Component Analysis (PCA) and wavelet transformation are the two popular methods to solve this problem. In the first part, I do Logistic Regression based on wavelet coefficients and using PCA to consider whether a person has AD as the response variable. In the second part, I use the linear model to consider the wavelet coefficients, which capture the features of brain image in wavelet domain, as the response variables. And then, compare the difference between AD patients and normal people based on T-Test. Finally, I will discuss the advantages and disadvantages of these analysis methods.