Exam 11: Simple Regression

You are interested in understanding why some people send more e-mail messages than others do.One possible explanation may be the age of the individual.Older people tend to be less computer savvy,and may have fewer friends who use e-mail.You examine the number of e-mails a person sends weekly using regression analysis and come up with the following equation of the regression line: Number of e-mails = 63 - 0.5 Age.Interpret these results.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose we have the following information from a simple regression: b₀= 117.4,b₁ = -14.39,s = 0.18,s = 0.18,n = 300, = 4.3,SST = 17,045,and SSE = 12,053. -Which of the following would most likely represent a 95% confidence interval for the estimate of y,given x = ?

Compute the value of the model error variance.

The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You are interested in determining the relationship between x and y.You have the following information: b₀= 117.4,b₁= -14.39,s = 0.18,s = 0.18,n = 300, = 4.3,SST = 17045,and SSE = 12053. -What is the sample mean of y?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The data below are for the number of unemployed persons (in millions)and the federal unemployment insurance payments (in billions of dollars)for the years 1978-1985.Some economists state that these two variables are positively related. -Test the null hypothesis that the true population coefficient of correlation equals zero using the 0.05 significance level.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose we have the following information from a simple regression: b₀= 117.4,b₁ = -14.39,s = 0.18,s = 0.18,n = 300, = 4.3,SST = 17,045,and SSE = 12,053. -Determine the sample mean of y.

What are the appropriate null and alternative hypotheses?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a regression analysis are listed below but,unfortunately,some values as identified by asterisks are missing. SUMMARY OUTPUT -Determine the mean square error.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: It was hypothesized that the number of bottles of an imported premium beer sold per evening in the restaurants of a city depends linearly on the average costs of meals in the restaurants.The following results were obtained for a sample of n = 20 restaurants,of approximately equal size, = 30.0, = 18.8, = 412, = 212 Where,y = Number of bottles sold per evening and x = Average costs,in dollars,of a meal. -Is it possible to provide a meaningful interpretation of the intercept of the sample regression line? Explain.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The data below are for the number of unemployed persons (in millions)and the federal unemployment insurance payments (in billions of dollars)for the years 1978-1985.Some economists state that these two variables are positively related. -What does the scatter diagram indicate about the relationship between these two variables?

You give a pre-employment examination to your applicants.The test is scored from 1 to 100.You have data on their sales at the end of one year measured in dollars.You want to know if there is any linear relationship between pre-employment examination score and sales.An appropriate test to use is the t-test on the population correlation coefficient.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: It was hypothesized that the number of bottles of an imported premium beer sold per evening in the restaurants of a city depends linearly on the average costs of meals in the restaurants.The following results were obtained for a sample of n = 20 restaurants,of approximately equal size, = 30.0, = 18.8, = 412, = 212 Where,y = Number of bottles sold per evening and x = Average costs,in dollars,of a meal. -Determine the sample regression line.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You want to explore the relationship between the grades students receive on their first quiz (x)and their first exam (y).The first quiz and test scores for a sample of eight students reveal the following summary statistics: -What is the covariance between x and y?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The below sample data set shows the relationship between two variables. -What is the value of cov(x,y)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: For a sample of 20 monthly observations a financial analyst wants to regress the percentage rate of return (y)of the common stock of a corporation on the percentage rate of return (x)of the Standard and Poor's 500 Index.The following summary statistics are available: , , ,and -Interpret the slope of the sample regression line.

The coefficient of determination can only take on positive values.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You are interested in determining the relationship between x and y.You have the following information: b₀= 117.4,b₁= -14.39,s = 0.18,s = 0.18,n = 300, = 4.3,SST = 17045,and SSE = 12053. -Using regression techniques,we can plot a scatter diagram and plot a line to the data using the Least Squares method.Generally,the points do not fall directly on the line.Why does this happen? Is it a problem?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The results of a regression analysis are listed below but,unfortunately,some values as identified by asterisks are missing. SUMMARY OUTPUT -Calculate the regression sum of squares.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that you are interested in the relationship between the return rate on a stock in 2010 compared to the return rate in 2009.You believe that the return rates in both years are positively correlated.A sample of 15 stocks yields the following regression results: b₀= 5.3,b₁= 1.04,s = 1.79,s = 0.2163,R² = 0.64,and MSE = 35.4. -How would you explain the slope coefficient b₁?