Question

CITY    SO2     MANUF   POP     TEMP    WIND    PRECIP-INCHES   PRECIP-#DAYS
Phoenix 11      213     582     70.3    6       7.05    36
Little Rock     15      91      132     61      8.2     48.52   100
San Francisco   16      453     716     56.7    8.7     20.66   67
Denver  24      454     515     51.9    9       12.95   86
Hartford        82      412     158     49.1    9       43.37   127
Wilmington      43      80      80      54      9       40.25   114
Washington      30      434     757     57.3    9.3     38.89   111
Jacksonville    18      136     529     68.4    8.8     54.47   116
Miami   14      207     335     75.5    9       59.8    128
Atlanta 32      368     497     61.5    9.1     48.34   115
Chicago 131     3344    3369    50.6    10.4    34.44   122
Indianapolis    40      361     746     52.3    9.7     38.74   121
Des Moines      20      104     201     49      11.2    30.85   103
Wichita 10      125     277     56.6    12.7    30.58   82
Louisville      35      291     593     55.6    8.3     43.11   123
New Orleans     9       204     361     68.3    8.4     56.77   113
Baltimore       47      625     905     55      9.6     41.31   111
Detroit 46      1064    1513    49.9    10.1    30.96   129
Minneapolis-St. Paul    42      699     744     43.5    10.6    25.94   137
Kansas City     18      381     507     54.5    10      37      99
St. Louis       61      775     622     55.9    9.5     35.89   105
Omaha   17      181     347     51.5    10.9    30.18   98
Albuquerque     15      46      244     56.8    8.9     7.77    58
Albany  56      44      116     47.6    8.8     33.36   135
Buffalo 11      391     463     47.1    12.4    36.11   166
Cincinnati      27      462     453     54      7.1     39.04   132
Cleveland       80      1007    751     49.7    10.9    34.99   155
Columbus        27      266     540     51.5    8.6     37.01   134
Philadelphia    79      1692    1950    54.6    9.6     39.93   115
Pittsburgh      63      347     520     50.4    9.4     36.22   147
Providence      136     343     179     50      10.6    42.75   125
Memphis 10      337     624     61.6    9.2     49.1    105
Nashville       23      275     448     59.4    7.9     46      119
Dallas  11      641     844     66.2    10.9    35.94   78
Houston 10      721     1233    68.9    10.8    48.19   103
Salt Lake City  28      137     176     51      8.7     15.17   89
Norfolk 38      96      308     59.3    10.6    44.68   116
Richmond        38      197     299     57.8    7.6     42.59   115
Seattle 40      379     531     51.1    9.4     38.79   164
Charleston      40      35      71      55.2    6.5     40.75   148
Milwaukee       20      569     717     45.7    11.8    29.07   123

Upload Pollution data, and perform Regression where you use the following variables, MANUF, POP, TEMP, WIND, PRECIP-INCHES,PRECIP-#DAYS, in order to predict SO2. Next, pick TWO variables with best P-value and perform another Regression Analysis, now using only these two variables.

I) What are the variables you picked? (10 points)

• a. MANUF, TEMP
• b. MANUF, WIND
• c. TEMP, WIND
• d. POP, PRECIP-INCHES
• e. None of the choices

II) After getting the new table, choose the variable with the LARGER coefficient. (10 points)

• a. POP
• b. MANUF
• c. TEMP
• d. PRECIP-INCHES
• e. None of the choices

III) How good is the fit and why? (10 points)

• a. Very good; P-values are extremely small
• b. Very good; R-square is in that range
• c. Good; Some P-values are small and some are not
• d. Poor; R-square is that range
• e. None of the choices

IV) Which of the two variables has a better P-value? (10 points)

• a. POP
• b. MANUF
• c. TEMP
• d. PRECIP-INCHES
• e. None of the choices

Answer 1

data

CITY	SO2	MANUF	POP	TEMP	WIND	PRECIP-INCHES	PRECIP-#DAYS
Phoenix	11	213	582	70.3	6	7.05	36
Little	15	91	132	61	8.2	48.52	100
San	16	453	716	56.7	8.7	20.66	67
Denver	24	454	515	51.9	9	12.95	86
Hartford	82	412	158	49.1	9	43.37	127
Wilmington	43	80	80	54	9	40.25	114
Washington	30	434	757	57.3	9.3	38.89	111
Jacksonville	18	136	529	68.4	8.8	54.47	116
Miami	14	207	335	75.5	9	59.8	128
Atlanta	32	368	497	61.5	9.1	48.34	115
Chicago	131	3344	3369	50.6	10.4	34.44	122
Indianapolis	40	361	746	52.3	9.7	38.74	121
Des	20	104	201	49	11.2	30.85	103
Wichita	10	125	277	56.6	12.7	30.58	82
Louisville	35	291	593	55.6	8.3	43.11	123
New	9	204	361	68.3	8.4	56.77	113
Baltimore	47	625	905	55	9.6	41.31	111
Detroit	46	1064	1513	49.9	10.1	30.96	129
Minneapolis-St.	42	699	744	43.5	10.6	25.94	137
Kansas	18	381	507	54.5	10	37	99
St.	61	775	622	55.9	9.5	35.89	105
Omaha	17	181	347	51.5	10.9	30.18	98
Albuquerque	15	46	244	56.8	8.9	7.77	58
Albany	56	44	116	47.6	8.8	33.36	135
Buffalo	11	391	463	47.1	12.4	36.11	166
Cincinnati	27	462	453	54	7.1	39.04	132
Cleveland	80	1007	751	49.7	10.9	34.99	155
Columbus	27	266	540	51.5	8.6	37.01	134
Philadelphia	79	1692	1950	54.6	9.6	39.93	115
Pittsburgh	63	347	520	50.4	9.4	36.22	147
Providence	136	343	179	50	10.6	42.75	125
Memphis	10	337	624	61.6	9.2	49.1	105
Nashville	23	275	448	59.4	7.9	46	119
Dallas	11	641	844	66.2	10.9	35.94	78
Houston	10	721	1233	68.9	10.8	48.19	103
Salt	28	137	176	51	8.7	15.17	89
Norfolk	38	96	308	59.3	10.6	44.68	116
Richmond	38	197	299	57.8	7.6	42.59	115
Seattle	40	379	531	51.1	9.4	38.79	164
Charleston	40	35	71	55.2	6.5	40.75	148
Milwaukee	20	569	717	45.7	11.8	29.07	123

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.803348342
R Square	0.645368558
Adjusted R Square	0.582786539
Standard Error	19.24789555
Observations	41
ANOVA
	df	SS	MS	F	Significance F
Regression	6	22923.23933	3820.539888	10.31236394	1.67991E-06
Residual	34	12596.37043	370.4814832
Total	40	35519.60976
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	145.9008608	62.22815407	2.344611743	0.025025544	19.43803635
MANUF	0.087686687	0.020710569	4.233910098	0.000164816	0.045597747
POP	-0.058150035	0.019901101	-2.921950643	0.006142514	-0.098593939
TEMP	-1.686881207	0.816914758	-2.064941526	0.046621439	-3.347051739
WIND	-3.767732623	2.386936211	-1.57848065	0.12371512	-8.618570632
PRECIP-INCHES	0.722776292	0.477060113	1.515063349	0.13899878	-0.246726503
PRECIP-#DAYS	-0.097826328	0.213064832	-0.459138786	0.649056535	-0.530826163

MANUF and POP have best p-values

e. None of the choices

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.750386655
R Square	0.563080131
Adjusted R Square	0.540084349
Standard Error	20.20892405
Observations	41
ANOVA
	df	SS	MS	F	Significance F
Regression	2	20000.38653	10000.19327	24.48623482	1.47107E-07
Residual	38	15519.22322	408.4006112
Total	40	35519.60976
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	34.72040499	5.01070221	6.929249342	3.06616E-08	24.57676868
MANUF	0.109977367	0.019174915	5.735481446	1.31297E-06	0.071159782
POP	-0.080097658	0.018657092	-4.293148113	0.000117237	-0.117866966

MANUF has largest coefficient

option B) is correct

c)

d. Poor; R-square is that range

d)

b. MANUF   has better p-values