Question

Determine if there is a linear relation among air temperature

x 1x1​,

wind speed

x 2x2​,

and wind chill y. The following data show the measured values for various days.

x 1x1

3030

negative 20−20

negative 30−30

3030

3030

00

negative 10−10

negative 30−30

00

negative 30−30

2020

negative 20−20

negative 10−10

1010

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x 2x2

3030

4040

7070

5050

2020

1010

5050

5050

4040

100100

9090

3030

2020

8080

y

00

negative 70−70

negative 96−96

negative 8−8

66

negative 22−22

negative 62−62

negative 88−88

negative 44−44

negative 104−104

negative 32−32

negative 64−64

negative 44−44

negative 44−44

​(a) Find the​ least-squares regression equation

ModifyingAbove y with caret equals b 0 plus b 1 x 1 plus b 2 x 2y=b0+b1x1+b2x2​,

where

x 1x1

is air temperature and

x 2x2

is wind​ speed, and y is the response​ variable, wind chill.

ModifyingAbove y with caretyequals=nothing plus+nothing x 1x1plus+nothing x 2x2

​(Round to three decimal places as​ needed.)

Answer 1

Following is the output of multiple regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.996290652
R Square	0.992595063
Adjusted R Square	0.99124871
Standard Error	3.258838207
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	2	15659.17971	7829.589854	737.2476785	1.91588E-12
Residual	11	116.8202911	10.62002646
Total	13	15776
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-25.01812022	1.838852973	-13.60528579	3.16915E-08	-29.06540833	-20.97083212
X1	1.33407627	0.040237161	33.1553277	2.24391E-12	1.245514875	1.422637665
X2	-0.414300042	0.033654276	-12.31047252	8.94273E-08	-0.488372605	-0.34022748

The least-squares regression equation line is

y' = -25.018+1.334*X1 - 0.414 * X2