Exam 16: A: Simple Linear Regression and Correlation

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. Salesperson Years of Exgperience Sales 1 0 7 2 2 9 3 10 20 4 3 15 5 8 18 6 5 14 7 12 20 8 7 17 9 20 30 10 15 25 -{Sales and Experience Narrative} Interpret the value of the slope of the regression line.

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

A regression analysis between weight (y in pounds)and height (x in inches)resulted in the following least squares line: $\hat { y } = 120 + 5 x$ .This implies that if the height is increased by 1 inch,the weight,on average,is expected to:

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?

The coefficient of correlation is used to determine:

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?

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.

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

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. Contestant Years of Education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 800 0 16 300 7 13 650 8 14 400 -{Game Winnings & Education Narrative} Predict with 95% confidence the winnings of a contestant who has 15 years of education.

Movie Revenues A financier whose specialty is investing in movie productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those movies 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 movie for ten recently released movies. Movie Cost of Twa Highest Paid Perfarmers ( \mil ) Grass Revenue () 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 0.7 58 -{Movie Revenues 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?

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

Grateful Dead Concert At a recent Grateful Dead 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.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below. AEe 62 57 40 49 67 54 43 65 54 41 Number af Concerts 6 5 4 3 5 5 2 6 3 1 Age 44 48 55 60 59 63 69 40 38 52 Number of Concerts 3 2 4 5 4 5 4 2 1 3 An Excel output follows: -{Grateful Dead Concert Narrative} Calculate the Pearson correlation coefficient and interpret.

The first-order linear model is sometimes called the simple linear regression model.

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

In a regression problem,if the coefficient of determination is 0.95,this means that:

Trivia Games & 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. Contestant Years of Education Winnings 1 11 750 2 15 400 3 12 600 4 16 350 5 11 800 0 16 300 7 13 650 8 14 400 -{Trivia Games & Education Narrative} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

The objective of a regression model is to analyze the relationship between two variables,x and y,both of which must be based on ____________________ data.

Movie Revenues A financier whose specialty is investing in movie productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those movies 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 movie for ten recently released movies. Movie Cost of Twa Highest Paid Perfarmers ( \mil ) Grass Revenue () 1 5.3 48 2 7.2 65 3 1.3 18 4 1.8 20 5 3.5 31 6 2.6 26 7 8.0 73 8 2.4 23 9 4.5 39 10 0.7 58 -{Movie Revenues Narrative} Predict with 95% confidence the gross revenue of a movie whose top two stars earn $5.0 million.

Grateful Dead Concert At a recent Grateful Dead 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.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below. AEe 62 57 40 49 67 54 43 65 54 41 Number af Concerts 6 5 4 3 5 5 2 6 3 1 Age 44 48 55 60 59 63 69 40 38 52 Number of Concerts 3 2 4 5 4 5 4 2 1 3 An Excel 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.

{Sales and Experience 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?