Curve Fitting Project - Linear Model

Date:  2021-04-05 06:56:27
2 pages  (431 words)
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(LR -1): Purpose: To analyse the winning times for the Olympic Men's Shot Put using a linear model.

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Data: The winning times were retrieved from http://www.databaseolympics.com/sport/sportevent.htm?sp=ATH&enum=300

OLYMPICS SHOT PUT MEN WINNING TIMES

YEAR TIME (SEC)

1948 17.12

1952 17.41

1956 18.57

1960 19.68

1964 20.33

1968 20.54

1972 21.18

1976 21.05

1980 21.35

1984 21.16

1988 22.47

1992 21.7

1996 21.62

2000 21.29

2004 21.16

2008 21.51

(LR-2): SCATTER PLOT

The winning time generally shows an upward trend and the trend is linear.

(LR 3): LINE OF BEST FIT (REGRESSION LINE)

y = 0.0667x - 111.45 where x = Year and y = Winning Time (in seconds)

(LR 4): SLOPE

The slant is 0.0667 and is certain since the triumphant circumstances are by and large expanding. The slant demonstrates that when all is said in done, the triumphant time increments by 0.0667 second a year, thus the triumphant time increments at a normal rate of 4(0.0667) = 0.2668 second every 4-year Olympic interim.

(LR 5): VALUES OF r2 AND rr2=0.673

We realize that the slant of the relapse line is certain so the relationship coefficient r must be sure.r = 0.673= 0.82

Review that r = 1 compares to immaculate positive relationship, thus r = 0.82 shows respectably solid positive connection (moderately near 1 yet not extremely solid).

(LR 6): FORECASTING

The regression line forecasts a winning time of 23.0172 seconds for Shot Put for the Men in the Olympics that took place in 2016.

(LR 7): NARRATIVE

The information comprised of the triumphant circumstances for the men's shot placed occasion in the Olympics from 1948 to 2008. The information shows a modestly solid upward straight pattern, looking in general at the 60 year time span.

We observe that r2 (which is a measure of how well a regression line approximates real data points) is 0.673. Thus, this indicates 67.3% change in one variable is explained by the change in second variable.

The relapse line predicts a triumphant time of 23.0172 seconds for the 2016 Olympics.

Take note of that there were some uncommon information purposes of 22.47 seconds in 1988 and 17.12 in 1948, which are far above and far underneath the relapse line.

On the off chance that we confine ourselves to taking a gander and no more late winning circumstances, past 1968, for Olympic winning circumstances in 1972 and past (10 winning circumstances), we have the accompanying scatter plot and relapse line.

Utilizing the latest ten winning times the regression line is y = 0.0149x - 8.3181.

When x = 2016, the prediction is y = 0.0149(2016) - 8.3181 =21.72 seconds.

This line forecasts a winning time of 21.72 seconds for 2016 and that would point towards a superb time.

Conclusion

I have analyzed two linear models, utilizing diverse subsets of the Olympic winning circumstances for the men's shot put. One model utilizes information reaching out back to 1948 and predicts a triumphant time of 23.0172 seconds for the 2016 Olympics, and the other model uses information from the latest 10 Olympic Games and forecasts 21.72 seconds.

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