Linear Regression!!!

Linear Regression Analysis

Introduction

Linear regression analysis is performed to ascertain whether or not a linear relationship exists between two variables - one of which is the explanatory variable or independent variable and the other is response or dependent variable . A linear regression model can be written as

y ax b

where x is explanatory variable or independent variable and y is response or dependent variable

In this study , it has been attempted to explore the relation ship between monthly household income and monthly expenditure on grocery in my locality

. It can be expected that monthly spending on grocery will increase with increasing monthly household income . Therefore , this can be a case of linear regression

Procedure

Data on average monthly household income and average monthly spending on grocery was collected from randomly selected 40 households in my area by personally contacting them over telephone . The data was entered in MS Excel spreadsheet . Monthly income (explanatory data ) data was entered into first column and monthly grocery expenditure data was entered in the second column The data is presented in appendix . A scatter plot was made using MS excel taking monthly income on x-axis and monthly expenditure on grocery on the y-axis . A linear trendline was superimposed on the scatter plot . The coefficients of the linear regression equation were calculated using MS office Excel . Besides regression analysis was performed on the data using MS Office Excel software . The results were analyzed and discussed

Results and Discussion

The regression equation is y 0 .2169x 201 .91

Here y is the monthly grocery bill of the house hold . This is the response or dependent variable

x is monthly income of the household . It is explanatory or independent variable . It can be concluded from this equation that for every incremental earning of a household there is an increase of 0 .2169 in the grocery bill of the household . This equation gives an expenditure of 201 .91 even for no income . This simply means whether or not you earn something there has to be some minimum expenditure on grocery

The results of Regression analysis is presented below

SUMMARY OUTPUT Regression Statistics Multiple R 0 .6 R Square 0 .2 Adjusted R Square 0 .1 Standard Error 132 .3296777 Observations 40

ANOVA

df SS MS F Significance F

Regression 1 1390376 .543 1390376 .543 79 . 7 .60828E-11

Residual 38 665423 .4566 17511 .14359 Coefficients Standard Error t Stat P-value Lower 95 Upper 95

Intercept 201 .9077501 82 . 2 .9 0 .4 35 368 .2608602

X Variable 1 0 .3 0 .8 8 .2 7 .60828E-11 0 .4 0 .3 From this analysis it is apparent the coefficients are of statistical significance as p-value corresponding to these coefficients is much smaller than 0 .05

The scatter diagram between the response variable - monthly grocery bill and the explanatory variable - monthly household income is presented below . The linear trend line is also imposed on the scatter diagram

The value of correlation coefficient r is 0 .82 . This value lies between -1...