Example: Simple Linear Regression
Example: Simple Linear Regression (2.08.14)
x is distance between the fire and the nearest fire station (miles)
y is damage in thousands of dollars
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For information about using XL in the solution, see:
For a basic view with a scatter plot and the fitted line use:
Stat/Regression/Fitted Line Plot
MTB > Note: x is distance between the fire and the nearest fire station (miles)
MTB > Note y is damage in thousands of dollars
MTB > %Fitline c2 c1;
SUBC> Confidence 95.0;
SUBC> Title "Damage vs Distance".
Regression
The regression equation is
y = 10.3 + 4.92 x
Predictor Coef StDev T P
Constant 10.278 1.420 7.24 0.000
x 4.9193 0.3927 12.53 0.000
S = 2.316 R-Sq = 92.3% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 841.77 841.77 156.89 0.000
Residual Error 13 69.75 5.37
Total 14 911.52
For a more complete evaluation as shown on the written example, use
Stat/Regression/Regression
Response: C2 [the column where I stored the dependent variable]
Predictor: C1 [the column where I stored the independent variable]
Graph:
Residuals for Plots Regular
Residual Plots: Normal Plot of Residuals & Residuals vs. Fits
Options:
Prediction Interval for New Observation In this case, use 3.5 with 95% confidence
Storage I checked all four [fits, sd of fits, confidence limits, prediction limits]
Results:
Regression Equation, Table of Coefficients, s, R-squared and Basic Analysis of Variance
Storage
Residuals, Fits, Standardized Residuals
MTB > Name c3 = 'FITS1' c4 = 'RESI1' c5 = 'SRES1' c6 = 'PFIT1' &
CONT> c7 = 'PSDF1' c8 = 'CLIM1' c9 = 'CLIM2' c10 = 'PLIM1' &
CONT> c11 = 'PLIM2'
MTB > Regress c2 1 c1;
SUBC> Fits 'FITS1';
SUBC> Residuals 'RESI1';
SUBC> SResiduals 'SRES1';
SUBC> GNormalplot;
SUBC> GFits;
SUBC> RType 1;
SUBC> Constant;
SUBC> Predict 3.5;
SUBC> PFits 'PFIT1';
SUBC> PSDFits 'PSDF1';
SUBC> CLimits 'CLIM1'-'CLIM2';
SUBC> PLimits 'PLIM1'-'PLIM2';
SUBC> Brief 2.
Regression Analysis
The regression equation is
y = 10.3 + 4.92 x
Predictor Coef StDev T P
Constant 10.278 1.420 7.24 0.000
x 4.9193 0.3927 12.53 0.000
S = 2.316 R-Sq = 92.3% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 841.77 841.77 156.89 0.000
Residual Error 13 69.75 5.37
Total 14 911.52
Predicted Values
Fit StDev Fit 95.0% CI 95.0% PI
27.496 0.604 (26.190, 28.801) (22.324, 32.667)
MTB >
MTB > print c1-c5
Data Display
Row x y FITS1 RESI1 SRES1
1 3.4 26.2 27.0037 -0.80365 -0.35921
2 1.8 17.8 19.1327 -1.33272 -0.61672
3 4.6 31.3 32.9068 -1.60685 -0.73813
4 2.3 23.1 21.5924 1.50761 0.68389
5 3.1 27.5 25.5279 1.97215 0.88173
6 5.5 36.0 37.3342 -1.33425 -0.64739
7 0.7 14.1 13.7215 0.37854 0.18972
8 3.0 22.3 25.0359 -2.73592 -1.22407
9 2.6 19.6 23.0682 -3.46819 -1.56097
10 4.3 31.3 31.4311 -0.13105 -0.05952
11 2.1 24.0 20.6085 3.39148 1.54912
12 1.1 17.3 15.6892 1.61081 0.77910
13 6.1 43.2 40.2858 2.91415 1.49866
14 4.8 36.4 33.8907 2.50928 1.16348
15 3.8 26.1 28.9714 -2.87139 -1.28850
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