Exam 11: Simple Regression

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below. -In a regression problem the following pairs of (x,y)are given: (2,1),(2,-1),(2,0),(2,-2)and (2,2).Which of the following is true of the given data?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below. -If the coefficient of determination is 1.0 in a regression problem,the:

What is the value of the test statistic F?

The coefficient of determination is the positive square root of the coefficient of correlation.

Calculate the regression sum of squares.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The manager of a used-car dealership is very interested in the resale price of used cars.The manager feels that the age of the car is important in determining the resale value.He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars)as the dependent variable and the age of the car (in years)as the independent variable.Unfortunately,the printout had lost some of the results,identified by"A" through"F".The partial results left are displayed below. -Which of the following is the value of "A"?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in determining the relationship between the amount spent on advertising and total sales.The manager collects data for the past 24 months and runs a regression of sales on advertising expenditures.The results are presented below but,unfortunately,some values identified by asterisks are missing. SUMMARY OUTPUT -Correlation analysis is used to determine the:

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. -Use these data to develop an estimated regression equation.

Regression analysis is used to measure the strength of the association between two numerical variables,while correlation analysis is used for prediction.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in determining the relationship between the amount spent on advertising and total sales.The manager collects data for the past 24 months and runs a regression of sales on advertising expenditures.The results are presented below but,unfortunately,some values identified by asterisks are missing. SUMMARY OUTPUT -What is the value of total sum of squares?

What is the p-value associated with the independent variable age?

Use the F-statistic from the analysis of variance table for regression to test H₀ : β₁ = 0 vs.H₁ : β₁ > 0 at α = 0.05.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in determining the relationship between the amount spent on advertising and total sales.The manager collects data for the past 24 months and runs a regression of sales on advertising expenditures.The results are presented below but,unfortunately,some values identified by asterisks are missing. SUMMARY OUTPUT -Calculate the standard error of estimate.

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. -Develop an approximation of the 95% confidence interval for the expected value of y,given x = .

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. -At the 0.05 level of significance,test the null hypothesis that the population slope is zero.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A sales manager is interested in determining the relationship between the amount spent on advertising and total sales.The manager collects data for the past 24 months and runs a regression of sales on advertising expenditures.The results are presented below but,unfortunately,some values identified by asterisks are missing. SUMMARY OUTPUT -A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: = 75 + 5x.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is:

The regression sum of squares (SSR)can never be larger than the total sum of squares.

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 happens to the width of a prediction interval for y as the x value on which the interval estimate is based gets farther away from the mean of x? Why?

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line: = 120 + 5x.This implies that if the height is increased by 1 inch,the weight is expected to:

When testing the strength of the relationship between two variables,the alternate hypothesis is H₁ ;ρ ≠ 0.