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, uneven bars and balance beam.

Simone constructs a linear regression model using Score on Uneven Bars as the explanatory variable and Score on Balance Beam as the response variable. A scatterplot of Simones data is shown.

Simone uses statistical software to fit a linear model to the data. A summary of that model fit is given below:

Coefficients	Estimate	Std Error	t value	Pr(>||)Pr(>|t|)
(Intercept)	5.801	2.384	2.433	0.0174
Score on Uneven Bars	0.5727	0.1655	3.461	0.000902

Residual standard error: 0.858 on 73 degrees of freedom Multiple R-squared: 0.141, Adjusted R-squared: 0.1292

1. Use the computer output to write the estimated linear regression equation for predicting Score on Balance Beam from Score on Uneven Bars.

= ____ +

Interpret the slope and intercept of the linear regression model:

2. An increase of 1 point in Score on Uneven Bars is associated with a(n) _?_ (increase, decrease) of ____ in Score on Balance Beam.

3. A gymnast who received a score of 0 points in Score on Uneven Bars would have an expected score of _____ in Score on Balance Beam.

4. Which of the following is the correlation coefficient for the linear relationship between Score on Balance Beam and Score on Uneven Bars?

A. -0.141 B. 0.3755 C. -0.3755 D. 0.141

5. What are the null and alternative hypotheses to test if there is a linear relationship between Score on Balance Beam and Score on Uneven Bars?

A. 0:1=0 vs. :10 B. 0:1=1 vs. :11 C. 0:1=0 vs. :10 D. 0:1=0 vs. :1>0

6. Based on the computer output, what is the test statistic for the test in part 5?

Test statistic: ________

7. Based on the computer output, the results of the hypothesis test tell us that we have _?_ (little, some, strong, very strong, extremely strong) evidence that there _?_ (is, is not) a linear relationship between Score on Balance Beam and Score on Uneven Bars.

8. In 2017, Melanie de Jesus dos Santos recieved a score of 14.466 on the uneven bars apparatus. Calculate the estimated value for this gymnasts score on balance beam that is predicted by the linear model.

Estimated value = ________

9. Melanie de Jesus dos Santoss actual score on balance beam that year was 14. 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, 11, of the regression line predicting Score on Balance Beam from Score on Uneven Bars.

IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places.( , )