The following bivariate data below is assumed to follow a li

The following bivariate data below is assumed to follow a linear regression model: y=+x This means that the data can be modeled as y i =+x i + i where the predicted dependent variable value for the i-th subject is y ˆ i =+x i and the residual (or error) is i .

y     

Run the linear regression using the technology of your choice. With the output, report the following accurate to 3 decimal places:
correlation: r=
intercept: =
slope: =

index number	x	y
1	53.3	54.9
2	45.7	60.2
3	46.2	55.1
4	39.9	56.5
5	58.6	57.2
6	62.2	64.8
7	45.5	63.4
8	44.8	62.4
9	49.9	59.8
10	59.7	68.7
11	36.5	57.2
12	36.2	54.6
13	46.7	51.8
14	73.7	67.8
15	57.8	63

Solution

Run the linear regression using the technology of your choice. With the output, report the following accurate to 3 decimal places:
correlation: r = 0.645
intercept: = 43.951
slope: = 0.315

Regression Analysis

r²

0.416

n

15

r

0.645

k

1

Std. Error

4.019

Dep. Var.

y     

ANOVA table

Source

SS

df

MS

F

p-value

Regression

149.8596

1  

149.8596

9.28

.0094

Residual

210.0097

13  

16.1546

Total

359.8693

14  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=13)

p-value

95% lower

95% upper

Intercept

43.9509

5.3147

8.270

1.55E-06

32.4691

55.4327

x    

0.3147

0.1033

3.046

.0094

0.0915

0.5379

Regression Analysis
	r²	0.416	n	15
	r	0.645	k	1
	Std. Error	4.019	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	149.8596	1	149.8596	9.28	.0094
Residual	210.0097	13	16.1546
Total	359.8693	14
Regression output				confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	43.9509	5.3147	8.270	1.55E-06	32.4691	55.4327
x	0.3147	0.1033	3.046	.0094	0.0915	0.5379