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Objective: To study the effect of explanatory variables on the explained variable with the

help of linear regression model & to analyze the effects of the explanatory variables.

Theory: In regression analysis, the key idea behind is the statistical dependence of one

variable, the independent variable, on one or more other variables, explanatory

variables. The two variable regression functions is given by-

Y= 0+ 1Xi+ui

Where, Y is called as the dependent variableXi is called as the independent variableUi is called as the random variable or stochastic variable

Project: In our project, we try to analyze the Mileage (MPG), in miles per gallon, of

passenger cars upon its various components-

i) Top Speed (SP), in miles per hour

ii) Horse Power (HP)

iii) Cubic feet of cab space or Volume of the engine (VOL)

iv) Weight of the vehicle (WT), in hundreds of pound

We develop the regression equation as

Y= 0+ 1Xi+2X2+3X3+4X4+ui

Where,

Y=Mileage of the car, in miles per gallon (MPG)

Xi =Top Speed of the vehicle (SP)

X2=Horse Power of the engine (HP)

X3=Cubic feet of engine cab space (VOL)

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X4=Weigh

t of the vehicle

(WT), in

hundreds of

pound

ui =Other

factors effectingMileage

Data:

SlNo.

MPG

SP

HP

VOL

WT

1 65.4 96 49 89 17.5

2 56 97 55 92 20

3 55.9 97 55 92 204 49 105 70 92 20

5 46.5 96 53 92 20

6 46.2 105 70 89 20

7 45.4 97 55 92 20

8 59.2 98 62 50 22.5

9 53.3 98 62 50 22.5

10 43.4 107 80 94 22.5

11 41.1 103 73 89 22.5

12 40.9 113 92 50 22.5

13 40.9 113 92 99 22.514 40.4 103 73 89 22.5

15 39.6 100 66 89 22.5

16 39.3 103 73 89 22.5

17 38.9 106 78 91 22.5

18 38.8 113 92 50 22.5

19 38.2 106 78 91 22.5

20 42.2 109 90 103 25

21 40.9 110 92 99 25

22 40.7 101 74 107 25

23 40 111 95 101 2524 39.3 105 81 96 25

25 38.8 111 95 89 25

26 38.4 110 92 50 25

27 38.4 110 92 117 25

28 38.4 110 92 99 25

29 46.9 90 52 104 27.5

30 36.3 112 103 107 27.5

31 36.1 103 84 114 27.5

32 36.1 103 84 101 27.5

33 35.4 111 102 97 27.5

34 35.3 111 102 113 27.5

35 35.1 102 81 101 27.5

36 35.1 106 90 98 27.5

37 35 106 90 88 27.5

38 33.2 109 102 86 30

39 32.9 109 102 86 30

40 32.3 120 130 92 30

41 32.2 106 95 113 30

42 32.2 106 95 106 30

43 32.2 109 102 92 30

44 32.2 106 95 88 30

45 31.5 105 93 102 30

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Note:

V0L=cubic feet of cabspace

HP= engine horse power

MPG=average miles pergallon

SP=top speed, miles perhour

WT=vehicle weight, hundreds ofpound

Regression statistics in SPSS sheet:

Variables Entered/RemovedModel Variables Entered Variables Removed Method

1 WT, VOL, SP, HP . Enter

a All requested variables entered.b Dependent Variable: MPG

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Model SummaryModel R R Square Adjusted R Square Std. Error of the

Estimate

1 .909 .827 .817 4.28

a Predictors: (Constant), WT, VOL, SP, HPb Dependent Variable: MPG

ANOVAModel Sum of

SquaresDf Mean

SquareF Sig.

1 Regression 6106.493 4 1526.623 83.409 .000

Residual 1281.193 70 18.303

Total 7387.687 74

a Predictors: (Constant), WT, VOL, SP, HPb Dependent Variable: MPG

CoefficientsUnstandardized Coefficients

StandardizedCoefficients

t Sig.

Model B Std. Error Beta

1 (Constant) 70.222 4.760 14.751 .000

SP -1.452E-02 .040 -.025 -.360 .720

HP -3.031E-02 .023 -.160 -1.347 .182

VOL -3.154E-02 .028 -.067 -1.117 .268

WT -.909 .138 -.733 -6.607 .000

a Dependent Variable: MPG

Residuals Statistics

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Normal P-P Plot of Regression Standardiz

Dependent Variable: MPG

Observed Cum Prob

1.00.75.50.250.00E

xpectedCumProb

1.00

.75

.50

.25

0.00

Minimum Maximum Mean Std. Deviation N

Predicted Value 7.80 48.62 34.67 9.08 75

Residual -4.96 16.78 9.71E-15 4.16 75

Std. PredictedValue

-2.958 1.537 .000 1.000 75

Std. Residual -1.159 3.921 .000 .973 75

a Dependent Variable: MPG

Charts:

Prediction:

i) From the SPSS output we found R2, the fitness of good, to be 0.827. This

signifies that the sample regression line fits the model very well.

ii) The value of F is found to be 83.409 & sig is equal .000. It means that the

mode is highly significant.

iii) The significance value are found to be .000, .720, .182, .268, .000 for const,

SP, HP, VOL & WT respectively. It means that Constant, HP & VOL values

are significant.

Summary: From the entire regression analysis we have seen that the out of four explanatory

variables, three variables are showing negative but significant value, So the Mileage of vehicles

are negatively related to SP, HP & VOL., but positively related to WT of the vehicle We can

conclude that the model is comparatively a good model.

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A PROJECT ON REGRESSION ANALYSIS

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By Jankim Hazarika

MBE 2nd semester

Roll no. 04