F-statistil vif (ml) 25.792770 22.834190 13.621363 2.389645 S. An avid fan of th

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F-statistil vif (ml) 25.792770 22.834190 13.621363 2.389645 S. An avid fan of the PGA tour with limited back RA VTINV DIPIN background in statistics h uestions in golf, na ylurive inportance of eack diferent aspect of the game on average ht i The following data on the top 196 tour players in 2006 can be found help in answering one of the age-old q in professional golf? web site in the file pgatour2006.csv: Y, PrizeMoney average prize money per tournament , Driving Accuracy is the percent of time a player is able to hit the fat his tee shot. ,GIR, Greens in Regulation is the percent of time a player was green in regulation. A green is considered hit in regulation if any part of the 0 o og e chap 6 7 8 9 10 11 12 0.0025 0.0035 0.0045 0.0055 RA VTINV 0.015 0.025 0.035 0.045 -450 -350 -250 DIPINV Figure 6.60 Plots of standardized residuals from model (6.38) HEAT

Explanation / Answer

The most common reason is,to make the variable normal.  First, even in OLS regression, the variables do not have to be normal, only the errors (estimated by the residuals) have to be normal. Second, it is better to use a method that fits the data then to make the data fit the method. So, if your residuals are markedly non-normal, use robust regression or quantile regression or maybe MARS.

The good reason for transforming is that it makes substantive sense. This is often the case when the variable involves money, because we tend to think about money in multiplicative terms rather than additive ones

There are seven independent variables and one reponse variable.

This is the problem of multiple regression.

From the given regression output the regression equation is,

ln(y) = -5603007 - 129745x1 + 557728x2 - 567684x3 + 257970x4 + 55178x5 + 309433x6 + 549595x7

b0 = -5603007

b1 = - 129745

b2 = 557728

b3 = - 567684

b4 = 257970

b5 = 55178

b6 =  309433

b7 =  549595

Overall significance :

Here we have to test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Assume alpha = level of significance = 0.05

Test statistic follows F-distribution.

F = 16.92

P-value = 2.2e-16 = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

Individual significance :

Here we have to test the hypothesis that,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Assume alpha = level of significance= 0.05

Test statistic follows t-distribution.

Decision rule :

If P-value < alpha then reject H0 at 5% level of significance otherwise accept H0.

Conclusion : The population slope for corresponding variable is differ than 0 or that variable is significant.

Now we can see that ln(x1), ln(x2), ln(x4) and ln(x6) are significant variables since P-value for all these variables is less than 0.05.

And remaining variablesln(x3), ln(x5) and ln(x7) are insignificant variables.

We included significant variables into model and excluded insignificant variables from the model.

R-sq = 0.3865

It expresses the proportion of variation in y which is expressed by variation in independent variables.

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