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? 100-Meter Freestyle Men Women 1980 50.40 54.79 1984 1988 1992 1996 2000 49.80 48.63 55.92 55.00 49.02 54.65 54.50 48.4853.83 53.84 53.12 The men's linear regression model is 48.74 (Round regression coefficients to three decimal places as needed.) 2004 48.17 2008

Explanation / Answer

using minitab

enter data

x   y
0   50.40
4   49.80
8   48.63
12   49.02
16   48.74
20   48.48
24   48.17
28   47.21

stat>regression>regression>fit regression model> response(y) predictor(x) >ok>ok

output as follows

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 5.7980 5.7980 39.99 0.001
x 1 5.7980 5.7980 39.99 0.001
Error 6 0.8700 0.1450
Total 7 6.6680

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.380786 86.95% 84.78% 76.35%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 50.107 0.246 203.85 0.000
x -0.0929 0.0147 -6.32 0.001 1.00

Regression Equation

y = 50.107 - 0.0929 x

Fits and Diagnostics for Unusual Observations

Obs y Fit Resid Std Resid
3 48.630 49.364 -0.734 -2.13 R

R Large residual

answer is

Regression Equation

y = 50.107 - 0.0923x

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.