# 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.

https://brainmass.com/statistics/confidence-interval/find-regression-lline-and-confidence-interval-477137

#### 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.