Stat1250_SGTA10

Excel code Result =T.DIST.2T(4.2961,41) 0.0001 =T.DIST.2T(1.8177,41) 0.0764 =T.DIST.2T(2.8495,41) 0.0068 =2*(1 NORM.DIST(1.96,0,1,TRUE)) ‐ 0.0500 =T.DIST.2T(0.6379,41) 0.5271 =T.INV(0.975,41) 2.0195 =NORM.INV(0.975,0,1) 1.9600 Research Question: Is there a relationship between household income and expenditure? 340 320 300 280 260 240 220 200 180 40 45 5055 6065 70 75 Annual Income ($'000 ) 100 50 0 40 50 60 70 80 ‐ 50 ‐ 100 Annual Income($'000) Residuals 12 10 8 6 4 2 0 ‐ 80 60 40 20020406080100 ‐ ‐ ‐ More © Copyright Macquarie University 3 Stat1250 SGTA 10: Linear Regression Testing the slope of a regression line As part of a study on poverty an economist was interested in knowing if there was a relationship between household income and expenditure for households with an income between $40,000 and $80,000 per annum. She obtained a random sample of 43 households with annual incomes within this range and, for each household, recorded the annual income ($’000) and the amount spent on food in one week. Reference: Selvanathan et al, Business Statistics Abridged , 6 th Edition, Cengage Learning, 2014 SUMMARY OUTPUT Regression Statistics R Square 0.165299635 Observations 43 Coefficients Standard Error t Stat P value ‐ Intercept 161.27613 37.54015762 4.296096 0.000104 Annual Income($'000) 1.817687813 0.637906051 * * Weekly Expenditure Food Residuals