Question

1. The following data refer to the SO2 concentration-time (t), temperature (T), relative humidity (RH), and atmospheric pressure (P) in the last 12 months:

Average monthly concentration (ppb)	Time	Temperature	RH (%)	Atmospheric pressure (mb)
10.3	1	14	31	980
9.9	2	17	42	1010
9.4	3	21	52	1003
10.6	4	28	63	1020
10.1	5	33	74	990
14.3	6	35	88	1050
13.3	7	36	84	1070
8.2	8	35	86	1025
8.8	9	32	90	995
9.1	10	27	81	1005
10	11	23	62	1080
10.4	12	18	42	1056

1. Fit a multiple linear regression model to estimate the SO2 concentration in the coming months.

Answer 1

You can do it in excel using Data Tab --> Data Analysis and then select Regression.

Below is its output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.755476222
R Square	0.570744322
Adjusted R Square	0.325455363
Standard Error	1.449166071
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	4	19.54609055	4.886522638	2.32682435	0.155339031
Residual	7	14.70057611	2.100082302
Total	11	34.24666667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-34.60977009	17.83193947	-1.940886472	0.093412987	-76.77560661	7.556066438	-76.77560661	7.556066438
Time	-0.328712315	0.193847552	-1.695725898	0.133757238	-0.787088939	0.129664309	-0.787088939	0.129664309
Temperature	0.051399637	0.212848653	0.241484437	0.816100937	-0.45190745	0.554706725	-0.45190745	0.554706725
RH (%)	0.006064122	0.085149601	0.071217271	0.945216837	-0.19528269	0.207410934	-0.19528269	0.207410934
Atmospheric Pressure	0.044296592	0.018176146	2.437072828	0.044951584	0.001316836	0.087276349	0.001316836	0.087276349

Thus the equation Average monthly concentration = -0.328*Time + 0.0514*Temperature + 0.0061*RH% + 0.0443*Atmospheric_pressure -34.601.

This regression can explain 32.54% of variation in Average monthly concentration. (Adjusted R-square)

Please upvote if it was helpful :)