Standing Reach in the NBA ~ Standing reach measures how high someone can reach with their hands while standing flat-footed. In basketball, a large standing reach can help a player get shots off against a defender, as well as increase their ability to block shots from opposing players. Arnold is a basketball fan who wonders if a player’s standing reach can be predicted from their wingspan. A person’s wingspan is the distance from the fingertips of one hand to the other when their straightened arms are raised parallel to the ground at shoulder height. Arnold obtains measurement data for players who were drafted by a National Basketball Association team between 2009 and 2017. He randomly selects 48 of these players to construct a linear regression model using Wingspan as the explanatory variable and Standing Reach as the response variable. A scatterplot of Arnold’s data is given below. Arnold fits a linear model to the data using the statistical software, R. A summary of that model fit is given below:
1. Use the computer output to write the estimated linear regression equation for predicting Standing Reach from Wingspan.
y^ = + x
2. Which of the following is the correlation coefficient for the linear relationship between Standing Reach and Wingspan?
A. -0.7814
B. 0.7814
C. 0.884
D. -0.884
3. Each additional 1 inch of Wingspan is associated with a(n) ? (increase/decrease) of inches in Standing Reach.
4. What is the expected Standing Reach if a player has a Wingspan of 0 inches?
5. The wingspan of Dakari Johnson is 86 inches. Calculate the estimated value for the standing reach of Dakari Johnson that is predicted by the linear model.
Estimated value =
6. Dakari Johnson’s standing reach is measured as 112 inches. Use this information and your result from part 5 to calculate the residual
for this player.
Residual =
7. What are the null and alternative hypotheses to test if there is a linear relationship between Standing Reach and Wingspan?
A. H0: b1 = 0 vs. HA: b1≠0
B. H0: β1 = 0 vs. HA: β1 > 0
C. H0: β1 = b1 vs. HA: β1≠ b1
D. H0: β1 = 0 vs. HA: β1≠ 0
8. Based on the computer output, what is the test statistic for the test in part 7?
Test statistic:
9. 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 Standing Reach and Wingspan.
10. Use information from the computer output to calculate a 95% confidence interval for the slope, β1, of the regression line predicting Standing Reach from Wingspan.
IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places.( ?, ?)