Determine if there is a linear relation among air temperature x 1 , wind speed x
ID: 3048728 • Letter: D
Question
Determine if there is a linear relation among air temperature x 1 , wind speed x 2 , and wind chill y. The following data show the measured values for various days. x 1 15 negative 5 negative 10 negative 5 5 0 0 15 10 negative 15 negative 15 negative 10 15 negative 15 x 2 10 10 20 25 40 20 5 25 45 50 35 15 15 25 y 3 negative 22 negative 35 negative 31 negative 22 negative 22 negative 11 negative 4 negative 16 negative 52 negative 48 negative 32 0 negative 44 (a) Find the least-squares regression equation ModifyingAbove y with caret equals b 0 plus b 1 x 1 plus b 2 x 2 , where x 1 is air temperature and x 2 is wind speed, and y is the response variable, wind chill. ModifyingAbove y with caret equalsnothingplusnothingx 1plusnothingx 2 (Round to three decimal places as needed.)
Explanation / Answer
Answer:
Determine if there is a linear relation among air temperature x 1 , wind speed x 2 , and wind chill y. The following data show the measured values for various days.
x1
x2
y
15
10
3
-5
10
-22
-10
20
-35
-5
25
-31
5
40
-22
0
20
-22
0
5
-11
15
25
-4
10
45
-16
-15
50
-52
-15
35
-48
-10
15
-32
15
15
0
-15
25
-44
Regression Analysis
R²
0.993
Adjusted R²
0.991
n
14
R
0.996
k
2
Std. Error
1.629
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,914.7949
2
1,957.3975
737.25
1.92E-12
Residual
29.2051
11
2.6550
Total
3,944.0000
13
Regression output
confidence interval
variables
coefficients
std. error
t (df=11)
p-value
95% lower
95% upper
Intercept
-12.5091
0.9194
-13.605
3.17E-08
-14.5327
-10.4854
x1
1.3341
0.0402
33.155
2.24E-12
1.2455
1.4226
x2
-0.4143
0.0337
-12.310
8.94E-08
-0.4884
-0.3402
(a) Find the least-squares regression equation ModifyingAbove y with caret equals b 0 plus b 1 x 1 plus b 2 x 2 , where x 1 is air temperature and x 2 is wind speed, and y is the response variable, wind chill. ModifyingAbove y with caret equalsnothingplusnothingx 1plusnothingx 2 (Round to three decimal places as needed.)
y = -12.509+1.334*x1+(-0.414)*x2
x1
x2
y
15
10
3
-5
10
-22
-10
20
-35
-5
25
-31
5
40
-22
0
20
-22
0
5
-11
15
25
-4
10
45
-16
-15
50
-52
-15
35
-48
-10
15
-32
15
15
0
-15
25
-44
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