5. Tennis magazine (Feb. 2000) claims that “tennis players who tie the knot ofte

Question

5.

Tennis

magazine (Feb. 2000) claims that “tennis players who tie the knot often see their games

unravel.” (In other words the player’s game worsens just after marriage) Use data in ‘Tennis’ sheet

which lists a sample of former players and their rankings on their wedding days and on their first

anniversaries. (If you are interested, try reading a journal article by Farrelly and Nettle. It discusses some

topics which we did not cover in class though

!)

a.

Construct a scattergram from the given data. Does it tend to support, or refute the magazine’s

claim? Justify your answer.

b.

Use simple linear regression to model the relationship between wedding day ranking (x) and

first anniversary ranking (y).

c.

Does the

linear model you developed in part b contribute information for predicting players’

rankings on their first anniversaries? Test at

5%

significance

level

.

d.

If the

player rankings don’t change (on average)

after getting married, what would the true

values of

0

and

1

Ranking onRanking on Wedding First Day 12 67 28 28 Player Anniversary 130 165 97 73 79 2 Arthur Ashe 3 Jonathan Stark 4 Richey Reneberg 5 Paul Haarhuis 6 Richard Fromberg 7 Byron Black 8 Sabine Appelmans 9 Petr Korda 10 Dominique Van Roost 43 11 Ivan Lendl 12 John McEnroe 13 Stefan Edberg 14 Chris Evert 15 Mats Wilander 16 Sandrine Testud 17 Zina Garrison 18 Yevgeny Kafelnikov 8 19 Boris Becker 20 Michael Stich 21 Julie Halard-Decugis 32 22 Todd Woodbridge 23 Jason Stoltenberg 16 49 4 4 12 4 4 14 15 15 27 31 71 82

Explanation / Answer

A)

A scatter plot (or scatter diagram) is a two-dimensional graphical portrayal of an arrangement of information. Every x/y variable is spoken to on the diagram as a speck or a cross. This kind of outline can be utilized as a part of to outwardly portray connections (relationship) between two numerical parameters or to speak to disseminations.

Scatter gram for the given information:

The correlation coefficient is a numerical incentive between - 1 and 1 that communicates the quality of the straight/linear connection between two factors. At the point when r is more like 1 it shows a strong positive relationship. An estimation of 0 shows that there is no relationship between the variables and Esteem near - 1 flag a solid negative connection between the two factors

r= nni=1 xi yi - ni=1 xi ni=1 yi / (nni=1 x2i   - (ni=1 xi )2 ) (n ni=1 y2i – (ni=1 yi)2)

In this way, utilizing the information esteems and equation r has a tendency to be r= 0.48 which demonstrates there is no connection between the two factors.

B) Simple Linear Regression is an approach to portray a connection between two factors through a condition of a straight line, called line best fit, that most nearly models this relationship.

The equation for the line of best fit: y= a + b x

Where

b= ni=1 xi yi – n x bar y bar/ ni=1 x2i – n x2 bar

and a= y bar – b x bar

Thus,

Mean x (x bar): 24.59

Mean y (y bar): 38.68

Intercept (a): 15.87

Slope (b): 0.9273

Regression Line Equation: y= 15.878 + 0.9273

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