\( (4 \text{ marks}) \text{ Let } (x_1, Y_1), (x_2, Y_2), \dots, (x_n, Y_n) \text{ be a random sample of size } n. \text{ A linear re-}\\
gression \text{ model without an intercept given by }\\\Y_i = \beta_1 x_i + \epsilon_i\\\text{is fitted to these paired observations. Here, } \beta_1 \text{ is the slope parameter while } \epsilon_1, \epsilon_2, \dots, \epsilon_n\\\text{are iid random errors with mean 0. Derive the least squares estimator of } \beta_1.