Use a graphing calculator to find a linear regression model for the men\'s 100-

Question

Use a graphing calculator to find a linear regression model for the men's 100- meter freestyle data given in the table on the right, where x is years since 1980 and y is winning time (in seconds). Do the same for the women's 100-meter freestyle data. Do these models indicate that the women will eventually catch up with the men? 1980 1984 1988 1992 1996 2000 2004 2008 100-Meter Freestyle Men 50.40 49.95 48.63 49.02 48.74 48.30 48.17 47.21 Women 54.79 55.92 55.00 54.65 54.50 53.83 53.84 53.12 The men's linear regression model is (Round regression coefficients to three decimal places as needed.)

Explanation / Answer

using minitab

a)

Source      DF Adj SS Adj MS F-Value P-Value
Regression   1 6.2872 6.2872    44.32    0.001
year       1 6.2872 6.2872    44.32    0.001
Error        6 0.8511 0.1419
Total        7 7.1383

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.376640 88.08%     86.09%      79.16%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant    241.7     29.0     8.34    0.000
year      -0.0967   0.0145    -6.66    0.001 1.00

Regression Equation

men = 241.7 - 0.0967 year

   y=24.170-0.097year

b)

Source      DF   Adj SS   Adj MS F-Value P-Value
Regression   1 0.04147 0.04147     1.66    0.226
supply     1 0.04147 0.04147     1.66    0.226
Error       10 0.24959 0.02496
Total       11 0.29107

Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.157985 14.25%      5.67%       0.00%

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant    2.826    0.400     7.06    0.000
supply    -0.0640   0.0497    -1.29    0.226 1.00

Regression Equation

price = 2.826 - 0.0640 supply

y=2.826-0.064supply

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