(Solved): (14 points) Stick the landing ~ Elite female gymnasts compete on 4 apparatus: Floor, Vault, Uneven ...

(14 points) Stick the landing ~ Elite female gymnasts compete on 4 apparatus: Floor, Vault, Uneven Bars, and Balance Beam. Simone is investigating the relationship between gymnasts' scores on the different apparatus. She collects a random sample of 75 gymnasts who competed in international competitions between the years 2006 and 2019. For this problem we will look at the scores for the two apparatus, vault and uneven bars. Simone constructs a linear regression model using Score on Vault as the explanatory variable and Score on Uneven Bars as the response variable. A scatterplot of Simone's data is shown. Coefficients Estimate Std Error t value Pr(> [r) 6.676 (Intercept) 2.814 2.373 0.0203 Score on Vault 0.5077 0.1956 2.596 0.0114 © Simone uses statistical software to fit a linear model to the data. A summary of that model fit is given below: Residual standard error: 1.168 on 73 degrees of freedom Multiple R-squared: 0.0845, Adjusted R-squared: 0.072 Elite Womens Gymnastics 1. Use the computer output to write the estimated linear regression equation for predicting Score on Uneven Bars from Score on Vault. ý= x 13.0 13.5 14.0 14.5 15.0 15.5 16.0 Score on Vault Interpret the slope and intercept of the linear regression model: 2. An increase of 1 point in Score on Vault is associated with a(n) ? 3. A gymnast who received a score of 0 points in Score on Vault would have an expected score of Estimated value= of 4. Which of the following is the correlation coefficient for the linear relationship between Score on Uneven Bars and Score on Vault? A. 0.0845 OB. -0.2907 C. 0.2907 D. -0.0845 7. Based on the computer output, the results of the hypothesis test tell us that we have ? linear relationship between Score on Uneven Bars and Score on Vault. in Score on Uneven Bars. 5. What are the null and alternative hypotheses to test if there is a linear relationship between Score on Uneven Bars and Score on Vault? A. Ho: 01 b1 vs. HA: 8101 B. Ho: 10 vs. HA: $10 C. Ho: $10 VS. HA: 51> 0 D. Ho: b10 vs. FA: 10 6. Based on the computer output, what is the test statistic for the test in part 5? Test statistic: ) in Score on Uneven Bars. evidence that there ? 8. In 2008, Jiang Yuyuan recieved a score of 14.825 on the vault apparatus. Calculate the estimated value for this gymnast's score on uneven bars that is predicted by the linear model. a 9. Jiang Yuyuan's actual score on uneven bars that year was 15.875. Use this information and your result from part 8 to calculate the residual for this gymnast. Residual = 10. Use information from the computer output to calculate a 99% confidence interval for the slope, 1, of the regression line predicting Score on Uneven Bars from Score on Vault. IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places. 1.1