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Find regression lline and confidence interval

Question 1: Suppose we have the following information from a simple regression:
-What is the coefficient of determination??
-What is the correlation coefficient?
-What is the sample mean of Y??
-Test the hypothesis vs. , with ? = 0.05.
 
Question 2: survey 35 students and find that the mean daily spending is $63.57 with a sample standard deviation of $17.32.  
-Develop a 95% confidence interval for the population mean daily spending.
-What level of confidence is associated with an interval of $58.62 to $68.52 for the population mean daily spending?
 
Question 3: wholesaler finds that 229 of the previous 500 calls to hardware store owners resulted in new product placements. Assume these 500 calls represent a random sample.

-Find a 95% confidence interval for the long-run proportion of new product placements.
-What level of confidence is associated with an interval of .400513 to .515487 for the long-run proportion of new
 
Question 4: The following results were obtained for a sample of n =20 restaurants of approximately equal size:
 
Where:
?y = Number of bottles of imported premium beer sold, and
?x = Average cost, in dollars, of a meal.
 
-Determine the sample regression line.
-Interpret the slope of the sample regression line.
-Is it possible to provide a meaningful interpretation of the intercept of the sample regression line? Explain.
 

Solution Preview

Hi there,

Question 1:
R^2=1-SSE/SST=1-12053/17045=0.292872.
The coefficient of determination (R^2) is 0.292872.
Since b1<0, it is a negative correlation. r=-sqrt(0.292872)=-0.541176.
The correlation coefficient is -0.541176.
Sample mean ?=b0+b1x=117.4-14.38*4.3=55.566
Null hypothesis: b1=0
Alternative hypothesis is b1>0 or b1<0.
This is a two tailed t test, the critical t value is 1.97 (degree of freedom N-2=298)
T=(b1-0)/Sb1=-14.39/3.20=-4.50.
Since the absolute value of test t value is bigger ...

Solution Summary

The solution provides detailed explanation how to find the regression line and confidence interval.

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