Question

In: Statistics and Probability

Q2: Using MS Excel Analyze a regression of Air Quality on three covariates CO2, NOx, and...

Q2: Using MS Excel Analyze a regression of Air Quality on three covariates CO2, NOx, and Sox

Data Set is as following

Air Quality

CO2

NOx

SOx

197

61

22

17

191

33

16

27

224

65

18

18

183

55

18

32

236

50

26

23

200

60

24

26

226

59

16

25

164

54

22

24

100

83

10

17

285

50

21

29

207

73

22

21

336

61

26

35

299

42

36

21

192

44

25

4

264

54

20

29

244

24

17

27

227

53

22

42

216

41

18

30

263

57

29

24

265

87

23

25

How to use CO2, NOx, and SOx to predict the Air Quality? Please provide the formula.

What is the correlations between Air Quality and each of the three factors? What do they mean?

What is the Coefficient of Determination (R Square) of the regression result? What does it mean?

Solutions

Expert Solution

Solution:
Go to data >data analysis >Regression

select Y as Air quality

Rest all as X variables

You will get'

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.739169
R Square 0.546371
Adjusted R Square 0.461316
Standard Error 38.24893
Observations 20
ANOVA
df SS MS F Significance F
Regression 3 28193.26 9397.755 6.423705 0.004621
Residual 16 23407.69 1462.98
Total 19 51600.95
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 40.78836 62.1144 0.656665 0.52073 -90.8883 172.465
CO2 -0.17858 0.591485 -0.30191 0.766606 -1.43247 1.075315
NOx 5.964901 1.605223 3.715932 0.001878 2.561979 9.367822
SOx 2.681185 1.136653 2.358843 0.031382 0.271589 5.090781

Regression equation is

Air quality=40.78836-0.17858*CO2+5.964901*NOx+2.681185*SOx

What is the correlations between Air Quality and each of the three factors? What do they mean?
Air Quality CO2 NOx SOx
Air Quality 1
CO2 -0.1844 1
NOx 0.614144 -0.12749 1
SOx 0.368603 -0.12929 -0.06312 1

there exists a negaive relationship between air quality and C02

there exists a positive relationship between air quality and NOx

there exists a positive relationship between air quality and SOx

Solutionc:

What is the Coefficient of Determination (R Square) of the regression result? What does it mean?

R sq=0.546371

=0.546371*100

=54.64% variation in Air quality is explained by model.

orchestra answered 1 year ago
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