Exam 8: Regression Wisdom

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

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?

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

The table below shows the gestation (in days)and average longevity (in years)for a number of different mammals: The scatter plot and regression equation are shown below: The regression analysis of this data yields the following values: R² = 0.9048 Use this model to predict the average longevity of an African elephant whose gestation is 660 days.

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

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. 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.

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

Over a period of years,a certain town observed the association between the number of people attending churches and the number of people in the city jail.The results are shown on the figure below.Also shown are the equation and R² value from a linear regression analysis.What is the best conclusion to draw from the figure?

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?

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.

Which of the labeled points below are influential points?

The table below shows the age and annual income of 12 randomly selected college graduates all living in the same city. The scatter plot and regression equation are shown below: The regression analysis of this data yields the following values: R² = 0.7182 Use this model to predict the annual income of a 56 year old college graduate living in this city.

The figure below examines the association between life expectancy and computer ownership for several countries.Also shown are the equation and R² value from a linear regression analysis.What is the best conclusion to draw from the figure?

The figure below shows the association between life expectancy and infant mortality 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?

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

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?

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?

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?

Which of the labeled points below are outliers?