Question

I Question 2 (20pts) Consider the following set of ordered pairs. Complete parts a through c. у Х 1 3 5 4 10 8 4 a) Calculate the slope and y-intercept for these data. (Round to four decimal places as needed.) b) Calculate the total sum of squares (SST). (Round to two decimal place as needed.) c) Partition the sum of squares into the SSR and SSE. (Round to three decimal places as needed.)

please show all the work. if you use excel please show the screenshots. Thank you !

Answer 1

Solution:

		$X^{^{2}}$	Y
1	1	1	1	1
3	4	9	16	12
5	10	25	100	50
4	8	16	64	32
$\sum X = 13$	$\sum Y = 23$	x2 = 51	ΣΥ? = 181	$\sum XY = 95$

(a)

$Slope (b)=\frac{n\sum (XY)-(\sum X)(\sum Y)}{[n(\sum X^{2})-(\sum X)^{2}]}$

  $= \frac{4(95)-(13)(23)}{4(51)-(13)^{2}}$

  $=\frac{380-299}{204-169}$

  $=\frac{81}{35}$

  

Y - intercept(a) ΣΥ ΣΧ - 6[= n η

$=\frac{23}{4}-(2.3143)(\frac{13}{4})$

  $=5.75-(2.3143)(3.25)$

  $=5.75-7.5215$

  $=-1.7715$

(b)

$SST = \sum_{i=1}^{n}(Y-\bar{Y})^{2}$

We have to calculate $\bar{Y}$ first

$\bar{Y}=\frac{\sum Y}{n}$

$=\frac{23}{4}$

  $=5.75$

$SST=22.5625+3.0625+18.0625+5.0625$

$SST=48.75$

(c)

We know that formula $SST=SSR+SSE$

$SSE=\sum Y^{2}-a(\sum Y)-b(\sum XY)$

$SSE=181-(-1.7715)(23)-(2.3143)(95)$

$SSE=181+40.7445-219.8585$

$SSE=221.7445-219.8585$

$SSE=1.886$

By the formula, we have to calculate SSR, so known values are SSR & SST

$SSR=SST-SSE$

$SSR=48.75-1.886$

$SSR=46.864$

NOTE:
If you have any doubt, Please comment below
I will clarify ASAP