class4b_regression_activities_engr195%28ii%29s10_sol

class4b_regression_activities_engr195%28ii%29s10_sol - i ))...

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ENGR 195(II) - Spring 2010 Class 4B - Linear Regression Activity 1 - Least Squares Method Activity 2 - Goodness of Fit i 1 1 0.5 1 0.5 1 -0.5 0.25 4 2 3 2.5 9 7.5 1.75 0.75 0.5625 0 3 5 2 25 10 2.5 -0.5 0.25 0.25 4 7 4 49 28 3.25 0.75 0.5625 2.25 5 9 3.5 81 31.5 4 -0.5 0.25 1 Sums: 25 12.5 165 77.5 1.875 7.5 Mean: 2.5 1. Compute the slope(a) and intercept(b) using the least squares method. (see Class 4b Slides for solution of simultaneous equations) a= 0.375 b= 0.625 3. Using the values in the table above compute the Sum of Squares of Errors. 2. Write the equation in y = ax + b form. SSE 1.875 y=0.375x+0.625 4. Using the values in the table above compute the Sum of the Squares of the Deviations SST 7.5 0.75 x i y i x i 2 x i y i f(x i ) predicted y e i e i 2 [ y i -y mean ] 2 1. Use your slope and intercept to compute predicted values of y for each x in the table above (called f(x
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Unformatted text preview: i )) 2. Compute the errors for each data point by calculating e i , e i 2 , and [y i-y mean ] 2 in the table above 5. Use SSE and SST to determine r 2 r 2 ENGR 195(II) - Spring 2010 Class 4B - Linear Regression - Activity 3 Year Telephone Expenditures 1981 360 1982 375 1983 415 1984 435 1985 455 1986 471 1987 499 1988 537 1989 567 1990 592 1991 618 1992 623 1993 658 1994 690 1995 708 1996 772 1997 809 1998 830 1999 849 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 0 100 200 300 400 500 600 700 800 900 f(x) = 27.4771929825x - 54086.8245614035 R = 0.9919889906 Trends in Telephone Expenditures Year Telephone expenditures (1999, 849) (1981, 360)...
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