Exam 16: Simple Linear Regression and Correlat

The following 10 observations of variables x and y were collected. a. Calculate the standard error of estimate. b. Test to determine if there is enough evidence at the 5% significance level to indicate that x and y are negatively linearly related. c. Calculate the coefficient of correlation, and describe what this statistic tells you about the regression line.

Sales and Experience The general manager of a chain of department stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected salespeople. These data are listed below. {Sales and Experience Narrative} Determine the least squares regression line.

Cost of Textbooks The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger textbooks will cost more money. As an experiment to analyze the claim, a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks. These data are listed below. {Cost of Textbooks Narrative} Interpret the value of the slope of the regression line.

Theatre Revenues A financier whose specialty is investing in stage productions has observed that, in general, movies with "big-name" stars seem to generate more revenue than those plays whose stars are less well known. To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the play for ten recently staged plays. {Theatre Revenues Narrative} Determine the least squares regression line.

To create a deterministic model, we start with a probabilistic model that approximates the relationship we want to model.

If the standard error of estimate is ____________________, this implies that the model's fit is poor.

If the coefficient of determination is 0.95, this means that 95% of the variation in the independent variable x can be explained by the y variable.

The least squares method for determining the best fit minimizes:

In regression analysis, the coefficient of determination R ² measures the amount of variation in y that is:

Income and Education A professor of economics wants to study the relationship between income ( y in $1000s)and education ( x in years). A random sample eight individuals is taken and the results are shown below. {Income and Education Narrative} Interpret the value of the slope of the regression line.

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t -table values listed below would be used?

The residual is defined as the difference between:

Rock Concert Revenues A financier whose specialty is investing in rock concerts has observed that, in general, concerts with "big-name" stars seem to generate more revenue than those concerts whose stars are less well known. To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the concert for ten concert tours. {Rock Concert  Revenues Narrative} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between payment to the two highest-paid performers and gross revenue.

You use a(n)____________________ interval whenever you want to estimate a one-time occurrence for a particular value of y when x is a given value.

If the coefficient of determination is 0.975, then which of the following is true regarding the slope of the regression line?

Sale and Experience The general manager of a chain of Designer stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected salespeople. These data are listed below. {Sales and Experience Narrative} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether more experience is related to higher sales, as the manager speculates.

Sales and Experience The general manager of a chain of department stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected salespeople. These data are listed below. {Sales and Experience Narrative} Predict with 95% confidence the monthly sales of a salesperson with 10 years of experience.

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

For a regression analysis to be valid, the error variable must have a(n)____________________ distribution.

You cannot interpret the ____________________ of the simple linear regression line unless the value of x = 0 lies within the range of where data was collected.