fix typo

tutorial_5_regression/tuto_5_regression.Rmd

@@ -304,7 +304,7 @@ What are the values of the $\beta_0$ and $\beta_1$ that minimizes the SSE?
 <details><summary>Solution</summary>
 <p>
 
-$$\hat{\beta}_1= \frac{\sum_{i=1}^n (y_i-\bar y)(x_i-\bar x)}{\sum_{i=1}^n (x_i-\bar x_i)^2}=\frac{\mbox{cor}(x,y)s_y}{s_x} $$
+$$\hat{\beta}_1= \frac{\sum_{i=1}^n (y_i-\bar y)(x_i-\bar x)}{\sum_{i=1}^n (x_i-\bar x)^2}=\frac{\mbox{cor}(x,y)s_y}{s_x} $$
 
 $$\hat{\beta}_0=\bar y - \hat{\beta}_1 \bar x $$
 
@@ -944,7 +944,7 @@ And we assume that $x_2 = x_1 + 1$.
 $$\log_2(\hat{y}_1) = 23.401 -1.615 \times \log_2(x_1)$$
 
 $$\log_2(\hat{y}_2) = 23.401 -1.615 \times \log_2(x_2)$$
-$$\log_2\left(\frac{\hat{y}_2}{\hat{y}_1} = \log_2(\hat{y}_2) - \log_2(\hat{y}_1) =  -1.615 (\log_2(x_2 - x_1) = -1.615 \times 1 = -1.615$$
+$$\log_2\left(\frac{\hat{y}_2}{\hat{y}_1}\right) = \log_2(\hat{y}_2) - \log_2(\hat{y}_1) =  -1.615 (\log_2(x_2 - x_1) = -1.615 \times 1 = -1.615$$
 
 ---