Exam 16: Simple Linear Regression and Correlation

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

Game Winnings & Education An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows. ​ ​ -{Game Winnings & Education Narrative} Estimate with 95% confidence the average winnings of all contestants who have 15 years of education.

We check for normality by drawing a pie chart of the residuals.

An inverse relationship between an independent variable x and a dependent variably y means that as x increases,y decreases,and vice versa.

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} Estimate the number of skin cancer cases per 100,000 people who live in a state that gets 6 hours of sunshine on average.

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

Accidents and Rain A statistician investigating the relationship between the amount of rain (in inches)and the number of automobile accidents gathered data on accidents in her city for 10 randomly selected days throughout the year.The results are shown below. ​ ​ -{Accidents and Rain Narrative} What does the slope of the least squares regression line tell you?

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

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} Use the residuals to compute the standardized residuals.

Consider the following data values of variables x and y. a.Calculate the coefficient of determination,and describe what this statistic tells you about the relationship between the two variables. b.Calculate the Pearson coefficient of correlation.What sign does it have? Why? c.What does the coefficient of correlation calculated tell you about the direction and strength of the relationship between the two variables?

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

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.

In a simple linear regression problem,the least squares line is ,and the coefficient of determination is 0.81.The coefficient of correlation must be −0.90.

We can often detect autocorrelation by graphing the residuals against ____________________.

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 relationship between quality and price per barrel. A partial Minitab 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.

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} Estimate the number of Allman Brothers concerts attended by a 64 year old person.

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 relationship between quality and price per barrel. A partial Minitab output follows: ​ ​ ​ -{Oil Quality and Price Narrative} For what values of API gravity degrees do we feel comfortable making predictions for oil price?

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} Does it appear that heteroscedasticity is a problem? Explain.

In order to predict with 80% 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?

In regression analysis,the coefficient of determination R² measures the amount of variation in y that is: