(LR-1)

I have selected data of Men's 100 Meter Winning Timings from year 1952 to 2008.

Data has been tabulated below:

Men's 100 Meter Winning Times
Year / Time in seconds
1952 / 10.4
1956 / 10.5
1960 / 10.2
1964 / 10
1968 / 9.95
1972 / 10.14
1976 / 10.06
1980 / 10.25
1984 / 9.99
1988 / 9.92
1992 / 9.96
1996 / 9.84
2000 / 9.87
2004 / 9.85
2008 / 9.69

(LR -2)

There is a decreasing trend in winning timings data. Trend seems to be linear.

(LR-3)

Regression line is y = -0.0104x + 30.619

Where x = year and y = winning timings in seconds

(LR-4)

Slope = -0.0104

It indicates that the winning time will decrease by 0.0104 seconds per year.

Since Olympics are conducted after 4 years. Change in winning time will be 4(0.0104) = 0.0416 seconds. Thus the winning time decreases by 0.0416 seconds on each 4-year interval.

(LR-5)

r² = 0.7098

Since there is a decreasing trend in data so coefficient of correlation will be negative.

r = √0.7098 = -0.8425

r is close to -1 so there is strong negative correlation between year and winning timings.

(LR-6)

Substitute x = 2012 in y = -0.0104x + 30.619

Predicted winning time for 2012

y = -0.0104(2012) + 30.619 ≈ 9.69

Predicted winning time for 2012 men’s 100 meter is 9.69 seconds.

(LR-7)

I have used Men's 100 Meter Winning Timings from year 1952 to 2008. From the scatter plot shown in LR-1, we can note that there is a decreasing linear trend in data.

I used the regression line to predict the winning time for 2012 men’s 100 meter. Predicted winning time for 2012 men’s 100 meter is 9.69 seconds which is the same as 2008 men’s 100 meter winning time.

The winning time for the year 1968 was low. Let us remove it and find the regression line again.

We can see that value of r² has increased.

r = √0.7829 = -0.8848

Substitute x = 2012 in y = -0.011x + 31.907

Predicted winning time for 2012

y = -0.011(2012) + 31.907 ≈ 9.78

Predicted winning time for 2012 men’s 100 meter is 9.78 seconds. Although the winning time has not decreased from before but the regression line fits the data well as coefficient of correlation is more close to -1.

Conclusion:

In this project, I have examined the men’s 100 meter winning time data. I have calculated two regression lines and both show a decreasing trend. There is a strong negative correlation between year and winning timings. From the first regression line the predicted winning time for 2012 men’s 100 meter is 9.69 seconds and from second regression line the predicted winning time for 2012 men’s 100 meter is 9.78 seconds. Actual winning time for men’s 100 meter in 2012 was 9.63. The regression line y = -0.0104x + 30.619 (shown in LR-3) gave more close result to actual winning time.