Project #29274 - Stats HW

Match each symbol with its name. 

s_e^2
b_1
r^2
b_0
E(Y|X)=beta_0+beta_1X+epsilon
beta_0
beta_1
r
e
sigma_e^2
y^^\^ = b_0 + b_1x


 
 
 
Question Part
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a) Two numerical variables have a negative correlation when:
    


b) The linear correlation between some response variable and its predictor is r = 0.00. Based on this we can conclude that:
    


c) Which of the following cannot be determined from a regression equation?
    


d) The managers at a local 5-star restaurant are considering the addition of 10 wines to their wine list. A 
sommelier at this establishment has reviewed and rated these wines. The ratings were on a 1 (very poor) to 9 (unsurpassed excellence) Likert scale. In addition to the sommelier's rating score, the wine's retail price was also recorded. A least squares regression linear model for price (Y) versus quality rating (X) resulted in a linear correlation coefficient of 0.96. 

Based on the correlation coefficient we can conclude that:
    
 
 
Question Part
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In a certain statistics class, past data has indicated that there is a positive, linear relationship between a student's midterm exam score and his/her subsequent final exam score. The regression line for this relationship is given by: 

final score = 40 + 0.6*(midterm score)

From the choices below, the best interpretation of the intercept is:
    


From the choices below, the best interpretation of the slope is:
    
 

 
Question Part
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A paper in the Journal of Human Movement Studies gave the following data on Y = judge's score and X = length of final step (in meters) for a sample of seven divers performing a forward pike with a single somersault:

 
X 1.17 1.19 0.9 0.88 0.67 0.74 0.97
Y 8.6 8.9 7.2 7.1 7.3 7.5 7.9


a) What is the sample correlation coefficient?  
(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  and  .

c) What is the estimated regression line? y hat =  +  x
(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 =  
(round to three decimal places)

e) Which of the following is the correct interpretation of the residual from (d)?
    
f) Find the estimated standard error of the residuals. se =  
round your answer to four decimal places

hint: look at pages 208 and 211 of yours notes

g) Construct a 99% confidence interval for the true slope of the regression line. 
 < beta_1 <  
(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?
    
i) What is the valid prediction range?  to  

j) What is the predicted score of a diver who takes a final step of x* = 0.83 meters? y hat* =  
(round to 2 decimal places)

k) Construct a 90% confidence interval for the true mean score of divers who take a final step of 0.83 meters.
 < E(y|x*) <  
(round your endpoints to 2 decimal places)

l) Construct a 90% prediction interval for an individual diver who takes a final step of 0.83 meters.
 <  y_p^*  <  
(round your endpoints to 2 decimal places)

Subject Mathematics
Due By (Pacific Time) 04/28/2014 11:00 pm
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