Determine the leastsquares regression line for the following

Determine the least-squares regression line for the following data: (x = 2, y = 10), (x = 3, y = 12), (x = 4, y = 20), and (x = 5, y = 16).

a. The estimated intercept is ____

b. The estimated slope is _____

Solution

Determine the least-squares regression line for the following data: (x = 2, y = 10), (x = 3, y = 12), (x = 4, y = 20), and (x = 5, y = 16).

a. The estimated intercept is 5.4

b. The estimated slope is    2.6

c. The sum of the squared deviations between y and is    25.2

Regression Analysis

r²

0.573

n

4

r

0.757

k

1

Std. Error

3.550

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

33.8000

1  

33.8000

2.68

.2431

Residual

25.2000

2  

12.6000

Total

59.0000

3  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=2)

p-value

95% lower

95% upper

Intercept

5.4000

5.8327

0.926

.4523

-19.6959

30.4959

x

2.6000

1.5875

1.638

.2431

-4.2302

9.4302

Observation

y

Predicted

Residual

resid square

1

10.0

10.6

-0.6

0.360

2

12.0

13.2

-1.2

1.440

3

20.0

15.8

4.2

17.640

4

16.0

18.4

-2.4

5.760

25.200

Regression Analysis
	r²	0.573	n	4
	r	0.757	k	1
	Std. Error	3.550	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	33.8000	1	33.8000	2.68	.2431
Residual	25.2000	2	12.6000
Total	59.0000	3
Regression output				confidence interval
variables	coefficients	std. error	t (df=2)	p-value	95% lower	95% upper
Intercept	5.4000	5.8327	0.926	.4523	-19.6959	30.4959
x	2.6000	1.5875	1.638	.2431	-4.2302	9.4302
Observation	y	Predicted	Residual	resid square
1	10.0	10.6	-0.6	0.360
2	12.0	13.2	-1.2	1.440
3	20.0	15.8	4.2	17.640
4	16.0	18.4	-2.4	5.760
				25.200