Question

The data The state of California operates numerous meteorological stations. One of the many functions of each station is to monitor rainfall on a daily basis. This information is then used to produce an average annual precipitation level for each station. CALIRAIN.txt lists average annual precipitation levels (in inches) for a sample of 30 meteorological stations scattered throughout the state. The data set contains average annual precipitation (y), and the most impact on the amount of rainfall at each station, as follows:

1. Altitude of the station (x1, feet)

2. Latitude of the station (x2, degrees)

3. Distance of the station from the Pacific coast (x3, miles)

Station Name    Precip  Altitude        Latitude        Distance        Shadow
1       Eureka  39.57   43      40.8    1       W
2       RedBluff        23.27   341     40.2    97      L
3       Thermal 18.20   4152    33.8    70      L
4       FortBragg       37.48   74      39.4    1       W
5       SodaSprings     49.26   6752    39.3    150     W
6       SanFrancisco    21.82   52      37.8    5       W
7       Sacramento      18.07   25      38.5    80      L
8       SanJose 14.17   95      37.4    28      L
9       GiantForest     42.63   6360    36.6    145     W
10      Salinas 13.85   74      36.7    12      L
11      Fresno  9.44    331     36.7    114     L
12      PtPiedras       19.33   57      35.7    1       W
13      PasaRobles      15.67   740     35.7    31      L
14      Bakersfield     6.00    489     35.4    75      L
15      Bishop  5.73    4108    37.3    198     L
16      Mineral 47.82   4850    40.4    142     W
17      SantaBarbara    17.95   120     34.4    1       W
18      Susanville      18.20   4152    40.3    198     L
19      TuleLake        10.03   4036    41.9    140     L
20      Needles 4.63    913     34.8    192     L
21      Burbank 14.74   699     34.2    47      W
22      LosAngeles      15.02   312     34.1    16      W
23      LongBeach       12.36   50      33.8    12      W
24      LosBanos        8.26    125     37.8    74      L
25      Blythe  4.05    268     33.6    155     L
26      SanDiego        9.94    19      32.7    5       W
27      Daggett 4.25    2105    34.1    85      L
28      DeathValley     1.66    -178    36.5    194     L
29      CrescentCity    74.87   35      41.7    1       W
30      Colusa  15.95   60      39.2    91      L

Answer 1

The data The state of California operates numerous meteorological stations. One of the many functions of each station is to monitor rainfall on a daily basis. This information is then used to produce an average annual precipitation level for each station. CALIRAIN.txt lists average annual precipitation levels (in inches) for a sample of 30 meteorological stations scattered throughout the state. The data set contains average annual precipitation (y), and the most impact on the amount of rainfall at each station, as follows:

1. Altitude of the station (x1, feet)

2. Latitude of the station (x2, degrees)

3. Distance of the station from the Pacific coast (x3, miles)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	R²	0.600
	Adjusted R²	0.554	n	30
	R	0.775	k	3
	Std. Error	11.098	Dep. Var.	Precip
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4,809.3560	3	1,603.1187	13.02	2.21E-05
Residual	3,202.2976	26	123.1653
Total	8,011.6536	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=26)	p-value	95% lower	95% upper
Intercept	-102.3574	29.2055	-3.505	.0017	-162.3902	-42.3247
Altitude	0.0041	0.0012	3.358	.0024	0.0016	0.0066
Latitude	3.4511	0.7949	4.342	.0002	1.8172	5.0849
Distance	-0.1429	0.0363	-3.931	.0006	-0.2176	-0.0682

The regression line is

Y=-102.3574+0.0041*x1+3.4511*x2-0.1429*x3

Calculated F= 13.02 , p=0.000 which is < 0.05 level of significance.

Ho is rejected.

The regression model is significant.

All x1, x2 and x3 are significant.

R square =0.600. 60% of variance in y is explained by the model.