A paper in the Journal of Human Movement Studies gave the following data on Y ud

Question

A paper in the Journal of Human Movement Studies gave the following data on Y udge's score and X length of final step (in meters) for a sample of seven divers performing a forward pike with a single somersault: a) What is the sample correlation coefficient? 0.803 (round your answer to 3 decimals) b) Based on this, we would describe the linear relationship between length of final step and judge's score as Positive and Strong c) What is the estimated regression line? 5.281 2,707 (round both regression coefficients to three decimals) d) What is the residual for the third diver, who took a final step of 0.9 meters? e3 -0.218 (round to three decimal places) e) Which of the following is the correct interpretation of the residual from (d)? o The third diver scored 0.218 points lower than expected based on the length of his final step. The third diver scored 0.218 points higher than expected based on the length of his final step. The third diver received the exact score predicted based on the length of his final step. The third diver's final step was 0.218 meters shorter than expected. The third diver's final step was 0.218 meters longer than expected. f) Find the estimated standard error of the residuals. Se (round your answer to four decimal places) g) Construct a 90% confidence interval for the true slope of the regression line (round the endpoints of your CI to two decimal places) h) Based on your confidence interval, can you conclude that there is there a significant relationship between length of diver's final step judge's score? Why or why not? No, since 0 is in the confidence interval. Yes, since 0 is not in the confidence interval. No, since 0 is not in the confidence interval. Yes, since 0 is in the confidence interval.

Explanation / Answer

From Excel

a) The correlation coefficient r=0.803

b)Since r=80% we conclude that there is strong positive correlation between two variables

c) The regression equation is

y=5.281+2.707 (x)

d) when x=0.9

y= 5.281+2.707 *(0.9)

y= 7.72

error or residual= actual-predicted =7.5-7.72= -0.218

SUMMARY OUTPUT Regression Statistics Multiple R 0.802659 R Square 0.644261 Adjusted R Square 0.573113 Standard Error 0.419086 Observations 7 ANOVA df SS MS F Significance F Regression 1 1.590404 1.590404 9.055251 0.029783 Residual 5 0.878167 0.175633 Total 6 2.468571 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.280932 0.856643 6.164683 0.001635 3.078861 7.483003 3.078861 7.483003 x 2.707401 0.899709 3.009194 0.029783 0.394624 5.020177 0.394624 5.020177

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