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    Find regression lline and confidence interval

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    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.
     

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    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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