Exam 16: Simple Linear Regression and Correlat

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

If the coefficient of correlation is 1.0, then the coefficient of determination must be 1.0.

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} Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a positive linear relationship exists between the quality of oil and price per barrel.

A prediction interval for a particular y is always ____________________ than a confidence interval for the mean of y .

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 standard error of estimate, and describe what this statistic tells you about the regression line.

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

The graph of a confidence interval for the expected value of y is represented by two parallel lines, one on either side of the regression line.

The point where confidence intervals and prediction intervals do best is .

In a simple linear regression problem, r and b₀ :

If the sum of squared residuals is zero, then the:

In a simple linear regression problem, the following sum of squares are produced: , , and . The percentage of the variation in y that is explained by the variation in x is:

The Pearson coefficient of correlation r equals one when there is no:

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} Determine the least squares regression line.

In the simple linear regression model, the slope represents the:

In the first-order linear regression model, the population parameters of the y -intercept and the slope are, respectively,

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} Estimate the monthly sales for a salesperson with 16 years of experience.

If the coefficient of determination is 0.95, this means that 95% of the y values were predicted correctly by the regression line.

The smallest value that the standard error of estimate s _e can assume is:

Wayne Newton Concert At a recent Wayne Newton 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: {Wayne Newton Concert 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?

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate s _e will be 0.0.