Exam 11: Two Quantitative Variables

Social warmth is a term referring to the feeling of being connected to others. A study published in PLoS One in 2016 looked at a potential relationship between physical warmth (body temperature) and social warmth among a group of 54 volunteers (Inagki et al.). These volunteers had their oral temperature taken by a registered nurse and then assessed themselves using a scale of 1 to 5 on twelve items related to a feeling of social connection for which the average was recorded. Higher average scores indicated higher levels of social warmth. The theory was that the thermoregulatory system, which helps maintain a relatively warm internal body temperature, may also help people assess feelings of social connection. Below is a scatterplot and least-squares regression line of the data. -State the null and alternative hypotheses for a simulation-based test of the slope using proper notation.

Observations with values of the explanatory variable near the mean of the explanatory variable may potentially be influential.

Annual measurements of the number of powerboat registrations (in thousands) and the number of manatees killed by powerboats in Florida were collected over the 14 years 1977-1990. A scatterplot of the data, least squares regression line, and correlation coefficient follow. -What is the predicted number of manatee deaths for a year with 600,000 powerboat registrations?

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data and a regression table from the Corr/Regression applet follows. -Which of the approaches to a test of the regression slope are valid?

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. -Is whether the mother smoked during pregnancy a confounding variable in describing the relationship between gestation period and birth weight?

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data and a regression table from the Corr/Regression applet follows. -A 95% confidence interval for the population slope is (-5.68, -4.73). How would you interpret this interval in the context of the study?

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. -Below is a picture of a simulated null distribution of correlation coefficients created using the Corr/Regression applet. How would you use this distribution to calculate the p-value?

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data follows. -Select the best explanation for how one sample would be simulated in order to generate the null distribution.

The graph below shows a scatter plot of medical expenses in the past year by age for a sample of Americans. Which one of the following is a true statement about the data shown in the graph?

The following scatterplot displays the finish time (in minutes) and age (in years) for the male racers at the 2018 Strawberry Stampede (a 10k race through Arroyo Grande).  Below are the same data for the female racers in this year's race. -The p-value for a simulation-based test of the correlation coefficient for the females is 0.213. We have evidence that there is no association between female ages and female race finish times.

Social warmth is a term referring to the feeling of being connected to others. A study published in PLoS One in 2016 looked at a potential relationship between physical warmth (body temperature) and social warmth among a group of 54 volunteers (Inagki et al.). These volunteers had their oral temperature taken by a registered nurse and then assessed themselves using a scale of 1 to 5 on twelve items related to a feeling of social connection for which the average was recorded. Higher average scores indicated higher levels of social warmth. The theory was that the thermoregulatory system, which helps maintain a relatively warm internal body temperature, may also help people assess feelings of social connection. Below is a scatterplot and least-squares regression line of the data. -Select the best explanation for how one sample would be simulated in order to generate the null distribution.

Annual measurements of the number of powerboat registrations (in thousands) and the number of manatees killed by powerboats in Florida were collected over the 14 years 1977-1990. A scatterplot of the data, least squares regression line, and correlation coefficient follow. -The y-intercept is not a valid prediction of manatee deaths. Why?

Which of the following correlation coefficient values describes the weakest linear association between two variables.

Are people with bigger brains more intelligent? Forty college students volunteered to participate in a study which examined brain size (measured as 1000's of pixels counted in a brain scan), and IQ scores (measured in points). A scatterplot of the data is shown below. -Select the best explanation for how one sample would be simulated in order to generate the null distribution.

Annual measurements of the number of powerboat registrations (in thousands) and the number of manatees killed by powerboats in Florida were collected over the 14 years 1977-1990. A scatterplot of the data, least squares regression line, and correlation coefficient follow. -The year 1984 had 559,000 powerboat registrations and 34 manatee deaths. Calculate the residual for this observation.

Babies born with low birth weights (less than 2500 grams) are at an increased risk for many infant diseases. Researchers in North Carolina collected data to see what variables may influence the birth weight (in grams) of a child, including whether the mother drank alcohol during pregnancy, whether the mother smoked during pregnancy, the mother's age (years), the gestation of the pregnancy (number of weeks from conception until birth), the mother's race, the length of the birth (hours), and several others. The plot below summarizes some of the variables measured. -How would the correlation coefficient between birth weight and gestation period computed from all women in the sample compare to the correlation coefficient between birth weight and gestation period computed from only non-smoking women?

If the correlation coefficient between variables x and y is equal to zero, then we can say that x and y are not associated.

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data follows. -State the null and alternative hypotheses using proper notation.

Data from gapminder.org on 184 countries was used to examine if there is an association between (average) female life expectancy (that is, the average lifespan of women in the country) and the average number of children women give birth to for the year 2019. A scatterplot of the data and a regression table from the Corr/Regression applet follows. -Using the regression table output, what is the standardized statistic for a test of the regression slope.

Social warmth is a term referring to the feeling of being connected to others. A study published in PLoS One in 2016 looked at a potential relationship between physical warmth (body temperature) and social warmth among a group of 54 volunteers (Inagki et al.). These volunteers had their oral temperature taken by a registered nurse and then assessed themselves using a scale of 1 to 5 on twelve items related to a feeling of social connection for which the average was recorded. Higher average scores indicated higher levels of social warmth. The theory was that the thermoregulatory system, which helps maintain a relatively warm internal body temperature, may also help people assess feelings of social connection. Below is a scatterplot and least-squares regression line of the data. -How would you interpret the slope of the regression line in the context of the study?