Exam 16: Simple Linear Regression and Correlation

The variance of the error variable is required to be constant.When this requirement is satisfied, the condition is called homoscedasticity.

The coefficient of correlation is used to determine:

If the regression line is horizontal, the slope is ____________________ and x and y are not related.

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken.Which of the following t-table values listed below would be used?

Correlation analysis is used to determine whether there is a linear relationship between an independent variable x and a dependent variable y.

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

In order to predict with 90% 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?

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

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} Plot the least squares regression line on the scatter diagram.

The unbiased estimator of the variance of the error variable is found by taking ____________________ divided by n - 2.

Marc Anthony Concert At a recent Marc Anthony 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: -{Marc Anthony Concert Narrative} Plot the residuals against the predicted values .

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} Determine the least squares regression line.

There is more error in estimating a mean value of y as opposed to predicting an individual value of y.

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.

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} Calculate the residual corresponding to the pair (x, y) = (8, 15).

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} Calculate the Pearson correlation coefficient.Interpret the results.

U V'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. -{Sales and Experience Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a positive linear relationship exists between years of experience and sales.

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

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} What does the value of the slope of the regression line tell you?

Truck Speed and Gas Mileage An economist wanted to analyze the relationship between the speed of a truck (x) and its gas mileage (y).As an experiment a truck is operated at several different speeds and for each speed the gas mileage is measured.These data are shown below. -{Truck Speed and Gas Mileage Narrative} What does the coefficient of correlation tell you about the direction and strength of the relationship between the two variables?