Question
In: Statistics and Probability
Summarizing Bivariate Data (1) The data in table below represent airline fuel cost per gallon (in...
Summarizing Bivariate Data
(1) The data in table below represent airline fuel cost per gallon (in dollars) for the US
domestic and international carriers with scheduled service by month from July 2014 to
December 2014.
Month Domestic (x) International (y)
July 3 2.84
August 2.98 2.84
September 2.89 2.81
October 2.69 2.67
November 2.58 2.55
December 2.3 2.3
(a) Find the correlation coefficient value r.
(b) If we wish to predict international cost using the domestic cost, identify response and
predictor.
(c) Find slope and intercept of the regression equation of y on x.
(d) Write out the regression equation of y on x.
Solutions
Expert Solution
Excel sheet: Values
| Sxx | Syy | Sxy | ||||||
| Domestic (X) | International (Y) | X2 | Y2 | XY | (X-Xbar)2 | (Y-Ybar)2 | (X-Xbar)(Y-Ybar) | |
| 3 | 2.84 | 9 | 8.0656 | 8.52 | 0.0676 | 0.029469 | 0.044633 | |
| 2.98 | 2.84 | 8.8804 | 8.0656 | 8.4632 | 0.0576 | 0.029469 | 0.0412 | |
| 2.89 | 2.81 | 8.3521 | 7.8961 | 8.1209 | 0.0225 | 0.020069 | 0.02125 | |
| 2.69 | 2.67 | 7.2361 | 7.1289 | 7.1823 | 0.0025 | 2.78E-06 | -8.3E-05 | |
| 2.58 | 2.55 | 6.6564 | 6.5025 | 6.579 | 0.0256 | 0.014003 | 0.018933 | |
| 2.3 | 2.3 | 5.29 | 5.29 | 5.29 | 0.1936 | 0.135669 | 0.162067 | |
| Total | 16.44 | 16.01 | 45.415 | 42.9487 | 44.1554 | 0.3694 | 0.228683 | 0.288 |
| Mean | 2.74 | 2.668333 | ||||||
| Variance | 0.061567 | 0.038114 | Slope | 0.779643 | ||||
| SD | 0.248126 | 0.195228 | intercept | 0.532112 | ||||
| Covariance | 0.048 | |||||||
| Correlation | 0.990893 |
Excel sheet: Formula
| Sxx | Syy | Sxy | ||||||
| Domestic (X) | International (Y) | X2 | Y2 | XY | (X-Xbar)2 | (Y-Ybar)2 | (X-Xbar)(Y-Ybar) | |
| 3 | 2.84 | =B3^2 | =C3^2 | =B3*C3 | =(B3-$B$10)^2 | =(C3-$C$10)^2 | =(B3-$B$10)*(C3-$C$10) | |
| 2.98 | 2.84 | =B4^2 | =C4^2 | =B4*C4 | =(B4-$B$10)^2 | =(C4-$C$10)^2 | =(B4-$B$10)*(C4-$C$10) | |
| 2.89 | 2.81 | =B5^2 | =C5^2 | =B5*C5 | =(B5-$B$10)^2 | =(C5-$C$10)^2 | =(B5-$B$10)*(C5-$C$10) | |
| 2.69 | 2.67 | =B6^2 | =C6^2 | =B6*C6 | =(B6-$B$10)^2 | =(C6-$C$10)^2 | =(B6-$B$10)*(C6-$C$10) | |
| 2.58 | 2.55 | =B7^2 | =C7^2 | =B7*C7 | =(B7-$B$10)^2 | =(C7-$C$10)^2 | =(B7-$B$10)*(C7-$C$10) | |
| 2.3 | 2.3 | =B8^2 | =C8^2 | =B8*C8 | =(B8-$B$10)^2 | =(C8-$C$10)^2 | =(B8-$B$10)*(C8-$C$10) | |
| Total | =SUM(B3:B8) | =SUM(C3:C8) | =SUM(D3:D8) | =SUM(E3:E8) | =SUM(F3:F8) | =SUM(G3:G8) | =SUM(H3:H8) | =SUM(I3:I8) |
| Mean | =B9/6 | =C9/6 | ||||||
| Variance | =(D9/6)-(B10^2) | =(E9/6)-(C10^2) | Slope | =I9/G9 | ||||
| SD | =SQRT(B11) | =SQRT(C11) | intercept | =C10-F11*B10 | ||||
| Covariance | =(F9/6)-(B10*C10) | |||||||
| Correlation | =B13/(B12*C12) |
a) r=0.99
b) Response: International carrier
Predictor: Domestic cost
c) Slope = 0.7796 and intercept = 0.5321
d) y=0.5321+0.7796 x
international carrier = 0.5321+0.7796 Domestic cost
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