How important are birdies (a score of one under par on a given golf hole)...

aortiH

aortiH

Answered

2021-02-21

How important are birdies (a score of one under par on a given golf hole) in determining the final total score of a woman golfer? From the U.S. Women’s OpenWeb site, we obtained data on number of birdies during a tournament and final score for 63 women golfers. The data are presented on the WeissStats CD. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Answer & Explanation

Alannej

Alannej

Expert

2021-02-22Added 104 answers

Given: n= Sample size =63 a) Birdies is on the horizontal axis and Score is on the vertical axis. image b) It is reasonable to find a regression lien for the data if there is no strong curvature present in the scatterplot. We note that there is no strong curvature in the scatterplot of part (a) and thus it is reasonable to find a regression line for the data. c) Let us first determine the necessary sums:  xi=570
 xi2=5646
 yi=18717
 xiyi=168943 Next, we can determine Sxx and Sxy
Sxx=  xi2  ( xi)2n=5646  570263=488.8751
Sxy=  xiyi  ( xi)( yi)n=168943  570  1871763= 401.2857 The estimate b of the slope β is the ratio of Sxy and Sxx: b= SxySxx= 401.2857488.8751= 0.8209 The mean is the sum of all values divided by the number of values: x=  xin= 57063=9.0476
y=  yin= 1871763=297.0952 The estimate a of the intercept α is the average of y decreased by the product of the estimate of the slope and the average of x. a= y  b x=297.0952  (0.8209)  9.0476=304.5221 General least-squares equation: y^= α + β x. Replace α by a=304.5221 and β by b= 0.8209 in the general least-squares equation: y=a + bx=304.5221 + (0.8209)x d) There appear to be no outliers, because no points in the graph deviate strongly from the general pattern in the other points. There appear to be no influential observatioons, because all data values lie near the regression line. e) Not applicable, because we concluded that there are no potential outliers in part (d). f) Not applicable, because we concluded that there are no potential outliers in part (d).

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