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Answer the following on regression and correlation.
Consider the following data: x y x - x̅ y - y̅ (x - x̅)² (y - y̅)² (x - x̅)(y - y̅) 2 6 3 4 4 1 6 1…
Consider the following data:
| $x$ | $y$ | $x - \bar{x}$ | $y - \bar{y}$ | $(x - \bar{x})^2$ | $(y - \bar{y})^2$ | $(x - \bar{x})(y - \bar{y})$ |
|---|---|---|---|---|---|---|
| $2$ | $6$ | |||||
| $3$ | $4$ | |||||
| $4$ | $1$ | |||||
| $6$ | $1$ |
(a)[1]
Calculate $\bar{x}$ and $\bar{y}$.
(b)[1]
Complete the table.
(c)[1]
Calculate $b_{xy}$.
Answer
Answer (a)
$\bar x=\frac{2+3+4+6}{4}=\frac{15}{4}=3.75$; $\bar y=\frac{6+4+1+1}{4}=3$.
Final answer: $\bar x=3.75,\ \bar y=3$
Answer (b)
| $x$ | $y$ | $x-\bar x$ | $y-\bar y$ | $(x-\bar x)^2$ | $(y-\bar y)^2$ | $(x-\bar x)(y-\bar y)$ |
|---|---|---|---|---|---|---|
| $2$ | $6$ | $-1.75$ | $3$ | $3.0625$ | $9$ | $-5.25$ |
| $3$ | $4$ | $-0.75$ | $1$ | $0.5625$ | $1$ | $-0.75$ |
| $4$ | $1$ | $0.25$ | $-2$ | $0.0625$ | $4$ | $-0.5$ |
| $6$ | $1$ | $2.25$ | $-2$ | $5.0625$ | $4$ | $-4.5$ |
| Total | $0$ | $0$ | $8.75$ | $18$ | $-11$ |
Answer (c)
$b_{xy}=\frac{\sum(x-\bar x)(y-\bar y)}{\sum(y-\bar y)^2}=\frac{-11}{18}$.
Final answer: $-\frac{11}{18}$