In a study for the relationship between household income and lead in the city of
ID: 3173351 • Letter: I
Question
In a study for the relationship between household income and lead in the city of Michigan a sample of households were studied as shown in the table below: You were asked to develop model/equation to describe this relationship. Sigma^n _i = 1 x _i = 262. sigma^n _i = 1 y _i = 983, sigma^n _i = 1 x_i y _i = 20711, sigma^n _i = 1 x^2 _i = 9404, sigma^n _i = 1 I^2 _i = 106749 Calculate the least squares estimated of the slope and intercept of the fitted linear model identifying the relationship between income and water lead levels. For a house with water lead level of 15 ppb, what would the expected income be for that household? Calculate the residuals for a observations, what can you say about that?Explanation / Answer
1) here b1=Sxy/SSx=-1985.98
bo=Ybar-b1*Xbar=150332.73
hence regression equztion y= -1985.98X+150332.73
b) expected income =-1985.98*15+150332.73=120543
c) residuals are given in colum Y-Yi' ' whcih reflects the shift of regression model from actual values.
x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi') 2.00 148000.00 585.64 2470090000.00 -4885410600.00 146360.8 -1639.23 5.00 135000.00 449.44 1346890000.00 -3607426500.00 140402.8 5402.82 10.00 132000.00 262.44 1135690000.00 -3312373000.00 130472.9 -1527.09 20.00 114000.00 38.44 246490000.00 -1542996000.00 110613.1 -3386.91 25.00 96000.00 1.44 5290000.00 226032500.00 100683.2 4683.18 30.00 94000.00 14.44 18490000.00 422561000.00 90753.27 -3246.73 35.00 83000.00 77.44 234090000.00 1503454500.00 80823.36 -2176.64 40.00 73000.00 190.44 640090000.00 2485978000.00 70893.45 -2106.55 45.00 61000.00 353.44 1391290000.00 3664911500.00 60963.54 -36.46 50.00 47000.00 566.44 2631690000.00 5040225000.00 51033.63 4033.63 Total 262.00 983000.00 2539.60 10120100000.00 -5043600.00 -5.8208E-11 mean 26.20 98300.00 SSx Ssy Sxy