hw1 110590049

tags data

2023 Educational Data Mining and Applications HW1.pdf

2.2(e)

Five number summary: min, Q1, median, Q3, max

2.2(f)

2.8(a)

following 2D data set
x={1.4,1.6}

Manhattan distance

$$d(x,y)=\sum _{i=0}^n|x_i-y_i|$$

Euclidean distance

$$d(x,y)=\sqrt[2]{\sum _{i=0}^n(x_i-y_i{)}^2}$$

supremum distance

$$d(x,y)=\underset{i=0}{\overset{n}{\max }}|x_i-y_i|$$

cosine similarity

$$d(x,y)=\frac{x\cdot y}{||x||\times ||y||}$$

2.8(b)

$$normalize(x)=\frac{x}{\sqrt[2]{{\sum }_{i=0}^n(x_i{)}^2}}$$

3.3(a)

3.3(b)

find the outlier value using the IQR method: $$\begin{gathered} IQR=Q3-Q1=35-20=15 \\ \begin{array}{rl}\text{Lower Bound}& =Q1-1.5\ast IQR\\ & =20-1.5\ast 15=20-22.5=-2.5\end{array} \\ \begin{array}{rl}\text{Upper Bound}& =Q3+1.5\ast IQR\\ & =35+1.5\ast 15=35+22.5=57.5\end{array} \\ 70>\text{Upper Bound} \\ \text{70 is the outlier value} \end{gathered}$$

3.7(a)

$$\begin{array}{rl}\text{min-max-normalizaion}& =\frac{x-min}{max-min}\\ & =\frac{35-13}{70-13}\\ & =0.3859\end{array}$$

3.7(b)

$$\begin{gathered} \mu =29.96,\sigma =12.7 \\ \begin{array}{rl}\text{z-index}& =\frac{x-\mu }{\sigma }\\ & =\frac{35-29.96}{12.7}\\ & =0.3968\end{array} \end{gathered}$$

3.8(b)

$$\begin{array}{rl}r& =\frac{\sum _i(x_i-\hat{x})(y_i-\hat{y})}{\sqrt{\sum _i(x_i-\hat{x}{)}^2}\sqrt{\sum _i(y_i-\hat{y}{)}^2}}\\ & =\frac{1590.6}{\sqrt{2910}\sqrt{1256.731}}\\ & =0.8329\end{array}$$ $$\begin{array}{rl}cov(x,y)& =\frac{1}{n}\sum _i((x_i-E(x))(y_i-E(y))\\ & =99.41\end{array}$$

3.11(a)