Worksheet_10 Emily Meyer

Math 201 Worksheet 10 Name:__Emily Meyer_____________ Correlation and Regression The driving distance in yards, fairway accuracy as a percentage, and gender (Female=1 Male=2) for PGA and LPGA golfers in 2008 are given in the excel file Golf.xlsx . Open the data set in MINITAB and complete the following. 1. Draw the scatter plot of the driving distance versus accuracy by Gender. Comment on the scatter plot. The Scatterplot has a negative skew to both of the genders. 2. Unstack the data set so that male and female data on separate columns. - On Minitab output 3. Find the correlation between driving distance and the accuracy for females and males. Is there significant linear relation between driving distance and accuracy? Comment on your findings. Both correlations for the females and males are both negative correlations but the females are doing better than the males. The females p-value < 0.05 significant negative correlation between drive distance and accuracy. The males p-value is <0.05 they have a significant negative correlation between drive distance and accuracy but the females have a better p-value compared to the males. Females Males 320 300 280 260 240 220 80 75 70 65 60 55 50 Drive Accuracy% 1 2 Gender Scatterplot of Accuracy% vs Drive by Emily Meyer

Math 201 Worksheet 10 Name:__Emily Meyer_____________ 4. What are the response variable and the predictor variable? - Response is accuracy and the predictor is the driving distance 5. Find the equation of the least square regression line for the accuracy versus driving distance for females. Discuss the accuracy of the model. Assumption: response is normally distributed The p-value for the females is 0.396 which is greater than 0.05 the males p-value is 0.286 which is also greater than 0.05 therefore the driving distance is normally distributed for both females and males. Since p-value is zero the slope and intercepts are highly significant. Intercept is 130.89 and slope is -0.25649 the equation of the regression line accuracy = 130.89 – 0.25469 x (drive distance) 6. Find the equation of the least square regression line for the accuracy versus driving distance for males. Discuss the accuracy of the model. 280 270 260 250 240 230 220 210 99.9 99 95 90 80 70 60 50 40 30 20 10 5 1 0.1 Mean 246.8 StDev 9.494 N 157 AD 0.382 P-Value 0.396 Drive_1 Percent Normality Test for Females drive distance by Emily Meyer Normal 320 310 300 290 280 270 260 99.9 99 95 90 80 70 60 50 40 30 20 10 5 1 0.1 Mean 287.6 StDev 8.554 N 197 AD 0.442 P-Value 0.286 Drive_2 Percent Normality Test for males drive distance by Emily Meyer Normal

Math 201 Worksheet 10 Name:__Emily Meyer_____________ 17.8% of the variation in accuracy is explained by the linear relationship with the driving distance. 10. Draw the fitted line for the Male golfers. 36.9% of the variation in accuracy is explained by the linear relationship with the driving distance. Open the Golf_New.xlsx data set in SPSS and complete the following. 11. Draw the scatter plot of the driving distance versus accuracy by Gender. Comment on the scatter plot. 270 260 250 240 230 220 80 75 70 65 60 55 50 S 5.24641 R-Sq 17.8% R-Sq(adj) 17.3% Drive_1 Accuracy%_1 Fitted Line Plot by Emily Meyer Accuracy%_1 = 130.9 - 0.2565 Drive_1 320 310 300 290 280 270 260 80 75 70 65 60 55 50 S 4.34856 R-Sq 36.9% R-Sq(adj) 36.6% Drive_2 Accuracy%_2 Fitted Line Plot for males by Emily Meyer Accuracy%_2 = 174.9 - 0.3879 Drive_2

Math 201 Worksheet 10 Name:__Emily Meyer_____________ The Scatterplot has a negative trend to both of the genders 12. Find the correlation between driving distance and the accuracy for females and males. Is there significant linear relation between driving distance and accuracy? Comment on your findings. Correlation for females is -0.422 and highly significant and correlation for males is -0.608 and highly significant since p-value is almost 0 13. Find the equation of the least square regression line for the accuracy versus driving distance for females. Discuss the accuracy of the model.

Math 201 Worksheet 10 Name:__Emily Meyer_____________ Equation of the regression line is given by accuracy = 174.925 – 0.388 * drive Both slope and intercepts are highly significant since p-value is almost 0 15. Draw fitted lines for the Females and Males golfers.