Exam 8: Regression Wisdom

A reporter studied the causes of a fire to a house,and established a strong positive association between the damages $\text { (in dollars) }$ and the number of firefighters at the scene.Describe three different possible cause-and-effect relationships that might be present.

Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I II III IV

The figure below shows the life expectancy for persons living in the U.S.A. The regression analysis of the data yields the following values: Variable Coefficient Constant -353.87 Year 0.2157 R2 = 0.9539 Use the regression model to predict the life expectancy in 2015.

A study of consumer behavior finds a strong positive association between sales of ice cream and sales of soda.Describe three different possible cause-and-effect relationships that might be present.

A college admissions officer in the U.S.A.,defending the college's use of SAT scores in the admissions process,produced the graph below.It represents the mean GPAs for last year's freshmen,grouped by SAT scores.It shows that increased SAT score is associated with increased GPA.What concerns you about the graph,the statistical methodology,or the conclusion reached?

The scatterplot below displays the yearly production in millions of pounds of flue-cured tobacco in the U.S.For what range of years is a linear model appropriate?

Which of the labeled points below are outliers?

The data in the table below can be used to explore the association between the rate of television ownership and per capita gross domestic product for several countries. TVs per 1000 per capita GDP (USD) Algeria 105 5500 Australia 554 23,200 China 321 3,600 Dominican Republic 95 5,700 Hungary 435 11,200 Italy 528 22,100 Russia 410 7,700 Syria 70 3,100 United States 806 36,200 a)Make a scatterplot showing the trend in television ownership versus per capita GDP.Describe what you see. b)Determine the correlation and comment on its significance. c)Find the equation of the line of regression.Interpret the slope of the equation. d)Use your model to predict the rate of TV ownership for India,which has a per capita GDP of $2,200.How much confidence do you have in this prediction? Explain. e)Discuss the impact that the U.S.A.data exerts on the model.

A study finds a strong positive association between size of children's feet and results in spelling tests.Describe three different possible cause-and-effect relationships that might be present.

The figure below shows the recent trend in first-birth rate for women in the U.S.A.between the ages of 18 and 19.(The first-birth rate is the number of 18 to 19 year-olds per 1000 who give birth to their first child). The regression analysis of this data yields the following values: Variable Coefficient Constant 1509.5 Year -0.725 R2 = 0.6174 Use this model to predict the first-birth rate for 18 to 19 year-olds in 2006.

The table below shows the age and annual income of 12 randomly selected college graduates all living in the same city. Age Annual Income (dollars) 26 28,520 31 36,750 55 72,155 47 43,225 38 34,197 50 60,030 29 31,625 33 55,975 40 37,064 52 75,082 25 19,055 The scatter plot and regression equation are shown below: The regression analysis of this data yields the following values: Variable Coefficient Constant -8447.05 Age 1380.95 R2 = 0.7182 Use this model to predict the annual income of a 56 year old college graduate living in this city.

Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I II III IV

The scatterplot below shows the percentage of the US population that is foreign born for the years 1910 - 1990.For what range of years is a linear model appropriate?

An economist noticed that nations with more TV sets have higher life expectancy.He established a strong positive association between length of life and number of TV sets.Describe three different possible cause-and-effect relationships that might be present.

Which of the labeled points below are influential points?

The scatterplot below displays world population (in millions)for the years 0 - 1800.Where the population is an estimate,the lower estimate is given.For what range of years is a linear model appropriate?

The scatterplot below displays the average longevity (in years)plotted against gestation (in days)for a number of different mammals.For what range of gestation lengths is a linear model appropriate?

Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I II III IV

The figure below shows the association between female life expectancy and the average number of children women give birth to for several different countries.Also shown is the equation and correlation from a regression analysis.What is the correct conclusion to draw from the figure?

The scatterplot below displays the total home attendance (in millions)for major league baseball's National League for the years 1960 through 2002.This total home attendance is the grand total of all attendees at all National League games during the season.For what range of years is a linear model appropriate?