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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