diff --git a/tutorial_5_regression/tuto_5_regression.Rmd b/tutorial_5_regression/tuto_5_regression.Rmd index 48dfe25fa5f761ac9ec9170e46d8e6f3ff30db18..f6de19f8550b5acd7d7d49ed9158d0711788f87d 100644 --- a/tutorial_5_regression/tuto_5_regression.Rmd +++ b/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 $x_2 = x_1 + 1$. $$\log_2(\hat{y}_1) = 23.401 -1.615 \times \log_2(x_1)$$ $$\log_2(\hat{y}_2) = 23.401 -1.615 \times \log_2(x_2)$$ -$$\log_2\left(\frac{\hat{y}_2}{\hat{y}_1} = \log_2(\hat{y}_2) - \log_2(\hat{y}_1) = -1.615 (\log_2(x_2 - x_1) = -1.615 \times 1 = -1.615$$ +$$\log_2\left(\frac{\hat{y}_2}{\hat{y}_1}\right) = \log_2(\hat{y}_2) - \log_2(\hat{y}_1) = -1.615 (\log_2(x_2 - x_1) = -1.615 \times 1 = -1.615$$ ---