Exam 16: Simple Linear Regression and Correlat

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} Calculate the Pearson correlation coefficient. Interpret this result.

Sunshine and Melanoma A medical researcher wanted to examine the relationship between the amount of sunshine ( x )in hours, and incidence of melanoma, a type of skin cancer ( y ). As an experiment he found the number of melanoma cases detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below. {Sunshine and Melanoma Narrative} Draw a scatter diagram of the data and plot the least squares regression line on it.

The value of the sum of squares for regression SSR can never be larger than the value of total sum of squares SST.

UV's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's ( x )and incidence of skin cancer ( y ). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country. These data are shown below. {UV's and Skin Cancer Narrative} Calculate the coefficient of determination and interpret it.

The prediction interval for a particular value of y is always wider than the confidence interval for mean value of y , given the same data set, x value, and confidence level.

Car Speed and Gas Mileage An economist wanted to analyze the relationship between the speed of a car ( x )and its gas mileage ( y ). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below. {Car Speed and Gas Mileage Narrative} Predict with 99% confidence the gas mileage of a car traveling 55 mph.

SSE stands for ____________________ of squares for ____________________.

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a positive relationship between quality and price per barrel. A partial statistical software output follows: {Oil Quality and Price Narrative} Determine the standard error of estimate and describe what this statistic tells you.

In regression analysis, the residuals represent the:

For a regression analysis to be valid, the error variable must have a mean of ____________________.

The coefficient of correlation is used to determine:

Graphically, a confidence interval for the mean of y is represented as two ____________________ lines.

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} Determine the coefficient of determination and discuss what its value tells you about the two variables.

In the simple linear regression model, the y -intercept represents the:

Cost of Books The editor of a major academic book publisher claims that a large part of the cost of books is the cost of paper. This implies that larger books 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 books. These data are listed below. {Cost of Books Narrative} Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years)and same confidence level? Why?

The value of the sum of squares for regression SSR can never be smaller than 0.0.

The coefficient of ____________________ measures the amount of variation in the dependent variable that is explained by the variation in the independent variable.

If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

Allman Brothers Concert At a recent Allman Brothers concert, a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year. The following data were collected: An Excel output follows: {Allman Brothers Concert Narrative} Interpret the value of the slope of 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 coefficient of determination and discuss what its value tells you about the two variables.