$1.$ Define machine learning and explain the difference between supervised, unsupervised, and reinforcement learning. Give example applications of each. $(5$ points$)$

$2.$ Differentiate between the training and testing phases in supervised learning. $(5$ points$)$

$3.$ Describe the basic idea of linear regression and its applications. $(5$ points$)$

$4.$ Given the set of data points below, calculate the coefficients $($slope and intercept$)$ of a simple linear regression model by hand. $(5$ points$)$

Data points: $\{(2,5),(3,8),(4,7),(5,10),(6,12),(7,14),(8,15)\}$