We often describe our emotional reaction to social rejection as "pain." Does social rejection cause activity in areas of the brain that are known to be activated by physical pain? If it does, we really do experience social and physical pain in similar ways. Psychologists first included and then deliberately excluded individuals from a social activity while they measured changes in brain activity. After each activity, the subjects filled out questionnaires that assessed how excluded they felt. Here are data for 13 subjects:

$$\begin{array}{ccc} \hline \text { SUBJECT } & \begin{array}{c} \text { SOCIAL } \\ \text { DISTRESS } \end{array} & \begin{array}{c} \text { BRAIN } \\ \text { ACTIVITY } \end{array} \\ \hline 1 & 1.26 & 0.055 \\ \hline 2 & 1.85 & -0.040\hspace{8pt} \\ \hline 3 & 1.10 & -0.026\hspace{8pt} \\ \hline 4 & 2.50 & -0.017\hspace{8pt} \\ \hline 5 & 2.17 & -0.017 \hspace{8pt}\\ \hline 6 & 2.67 & 0.017 \\ \hline 7 & 2.01 & 0.021 \\ \hline 8 & 2.18 & 0.025 \\ \hline 9 & 2.58 & 0.027 \\ \hline 10 & 2.75 & 0.033 \\ \hline 11 & 2.75 & 0.064 \\ \hline 12 & 3.33 & 0.077 \\ \hline 13 & 3.65 & 0.124 \\ \hline \end{array}$$

The explanatory variable is "social distress" measured by each subject's questionnaire score after exclusion relative to the score after inclusion. (So values greater than 1 show the degree of distress caused by exclusion.) The response variable is change in activity in a region of the brain that is activated by physical pain. Negative values show a decrease in activity, suggesting less distress. Discuss what the data show about the relationship between social distress and brain activity.

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay under water. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study gives a scatterplot for one penguin titled "The Relation of Dive Duration (y) to Depth (x)." Duration y is measured in minutes and depth x is in meters. The report then says, "The regression equation for this bird is:

$$\hat{y} = 2.69 + 0.0138x."$$

What is the slope of the regression line? Interpret this value.

We often describe our emotional reaction to social rejection as "pain." A clever study asked whether social rejection causes activity in areas of the brain that are known to be activated by physical pain. If it does, we really do experience social and physical pain in similar ways. Subjects were first included and then deliberately excluded from a social activity while changes in brain activity were measured. After each activity, the subjects filled out questionnaires that assessed how excluded they felt. Here are data for 13 subjects.

The explanatory variable is "social distress" measured by each subject's questionnaire score after exclusion relative to the score after inclusion. (So values greater than 1 show the degree of distress caused by exclusion.) The response variable is change in activity in a region of the brain that is activated by physical pain. Discuss what the data show. Follow the four-step process in your discussion.

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to the body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:

$$\begin{array}{lllllllll} \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 \\ \text { Percent heat loss from beak } & 32 & 34 & 35 & 33 & 37 & 46 & 55 & 51 \\ \hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 \\ \text { Percent heat loss from beak } & 43 & 52 & 45 & 53 & 58 & 60 & 62 & 62 \end{array}$$

Investigate the relationship between outdoor temperature and beak heat loss, as a percentage of total body heat loss.

A professor asked her sophomore students, "Does either of your parents allow you to drink alcohol around him or her?" and "How many drinks do you typically have per session? (A drink is defined as one 12 oz beer, one 4 oz glass of wine, or one 1 oz shot of liquor.)" Table 24.1 contains the responses of the female students who are not abstainers. 18 The sample is all students in one large sophomore-level class. The class is popular, so we are tentatively willing to regard its members as an SRS of sophomore students at this college. Does the behavior of parents make a significant difference in how many drinks students have on average?

Does the physiology of women make them better suited than men to long-distance running? Will women eventually outperform men in long-distance races? Researchers examined data on world record times (in seconds) for men and women in the marathon. Here are data for women:

$$\begin{array}{lccccccc} \text { Year } & 1926 & 1964 & 1967 & 1970 & 1971 & 1974 & 1975 \\ \text { Time } & 13,222.0 & 11,973.0 & 11,246.0 & 10,973.0 & 9990.0 & 9834.5 & 9499.0 \\ \hline \text { Year } & 1977 & 1980 & 1981 & 1982 & 1983 & 1985 & \\ \text { Time } & 9287.5 & 9027.0 & 8806.0 & 8771.0 & 8563.0 & 8466.0 & \end{array}$$

Here are data for men :

$$\begin{array}{lccccccc} \text { Year } & 1908 & 1909 & 1913 & 1920 & 1925 & 1935 & 1947 \\ \text { Time } & 10,518.4 & 9751.0 & 9366.6 & 9155.8 & 8941.8 & 8802.0 & 8739.0 \\ \hline \text { Year } & 1952 & 1953 & 1954 & 1958 & 1960 & 1963 & 1964 \\ \text { Time } & 8442.2 & 8314.8 & 8259.4 & 8117.0 & 8116.2 & 8068.0 & 7931.2 \\ \hline \text { Year } & 1965 & 1967 & 1969 & 1981 & 1984 & 1985 & 1988 \\ \text { Time } & 7920.0 & 7776.4 & 7713.6 & 7698.0 & 7685.0 & 7632.0 & 7610.0 \end{array}$$

(a) What do the data show about women's and men's times in the marathon? (Start by plotting both sets of data on the same plot, using two different plotting symbols.)

(b) Based on these data, researchers (in 1992) predicted that women would outrun men in the marathon in 1998. How do you think they arrived at this date? Was their prediction accurate? (You may want to look on the web; try doing a Google search on "women's world record marathon times.")

Does the physiology of women make them better suited than men to long distance running? Will women eventually outperform men in long-distance races? In 1992, researchers examined data on world record times (in seconds) for men and women in the marathon. Here are data for women:

$$\begin{array}{l|ccccccc} \hline \text { Year } & 1926 & 1964 & 1967 & 1970 & 1971 & 1974 & 1975 \\ \text { Time } & 13,222.0 & 11,973.0 & 11,246.0 & 10,973.0 & 9990.0 & 9834.5 & 9499.0 \\ \hline \text { Year } & 1977 & 1980 & 1981 & 1982 & 1983 & 1985 & \\ \text { Time } & 9287.5 & 9027.0 & 8806.0 & 8771.0 & 8563.0 & 8466.0 & \\ \hline \end{array}$$

Here are data for men:

$$\begin{array}{l|ccccccc} \hline \text { Year } & 1908 & 1909 & 1913 & 1920 & 1925 & 1935 & 1947 \\ \text { Time } & 10,518.4 & 9751.0 & 9366.6 & 9155.8 & 8941.8 & 8802.0 & 8739.0 \\ \hline \text { Year } & 1952 & 1953 & 1954 & 1958 & 1960 & 1963 & 1964 \\ \text { Time } & 8442.2 & 8314.8 & 8259.4 & 8117.0 & 8116.2 & 8068.0 & 7931.2 \\ \hline \text { Year } & 1965 & 1967 & 1969 & 1981 & 1984 & 1985 & 1988 \\ \text { Time } & 7920.0 & 7776.4 & 7713.6 & 7698.0 & 7685.0 & 7632.0 & 7610.0 \\ \hline \end{array}$$

(a) What do the data show about women's and men's times in the marathon? (Start by plotting both sets of data on the same plot, using two different plotting symbols.)

(b) Based on these data, researchers (in 1992) predicted that women would outrun men in the marathon in 1998. How do you think they arrived on this date? Was their prediction accurate? (You may want to look on the web; try doing a Google search on "women's world record marathon times.")

Find the x-intercept and the y-intercept of the graph of each equation. Then graph the equation.

y - x = -9

Jasmin is concerned about how much energy she uses to heat her home, so she keeps a record of the natural gas her furnace consumes for each month from October to May. Because the months are not equally long, she divides each month's consumption by the number of days in the month to get the average number of cubic feet of gas used per day. She wants to see if there is a relationship between gas consumption and the average temperature (in degrees Fahrenheit) for each month. The data are given in the table. Calculate the correlation.

$$\begin{array}{|l|c|c|} \hline \text { Month } & \begin{array}{c} \text { Average } \\ \text { temperature } \\ \left({ }^{\circ} \mathrm{F}\right) \end{array} & \begin{array}{c} \text { Average fuel } \\ \text { consumption } \\ \left(\mathrm{ft}^3 / \text { day }\right) \end{array} \\ \hline \text { October } & 49.4 & 520 \\ \hline \text { November } & 38.2 & 610 \\ \hline \text { December } & 27.2 & 870 \\ \hline \text { January } & 28.6 & 850 \\ \hline \text { February } & 29.5 & 880 \\ \hline \text { March } & 46.4 & 490 \\ \hline \text { April } & 49.7 & 450 \\ \hline \text { May } & 57.1 & 250 \\ \hline \end{array}$$

Joan is concerned about how much energy she uses to heat her home, so she keeps a record of the natural gas her furnace consumes for each month from October to May. Because the months are not equally long, she divides each month's consumption by the number of days in the month to get the average number of cubic feet of gas used per day. She wants to see if there is a relationship between gas consumption and the average temperature (in degrees Fahrenheit) for each month. The data are given in the table. Calculate the correlation.

$$\begin{array}{|l|l|l|} \hline \text { Month} & \text { Average temperature $\left(^{\circ} \mathrm{F}\right)$} & \text { Average fuel consumption $\left(f t^{3} / d a y\right)$}\\ \hline \text { October } & 49.4 & 520 \\ \hline \text { November } & 38.2 & 610 \\ \hline \text { December } & 27.2 & 870 \\ \hline \text { January } & 28.6 & 850 \\ \hline \text { February } & 29.5 & 880 \\ \hline \text { March } & 46.4 & 490 \\ \hline \text { April } & 49.7 & 450 \\ \hline \text { May } & 57.1 & 250 \\ \hline \end{array}$$

Have average global temperatures been increasing in recent years? Here are annual average global temperatures for the last 20 years in degrees Celsius.

$$\begin{array}{lcccccccccc} \text { Year } & 1994 & 1995 & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 & 2002 & 2003 \\ \text { Temperature } & 14.23 & 14.35 & 14.22 & 14.42 & 14.54 & 14.36 & 14.33 & 14.45 & 14.51 & 14.52 \\ \hline \text { Year } & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 & 2011 & 2012 & 2013 \\ \text { Temperature } & 14.48 & 14.55 & 14.50 & 14.49 & 14.41 & 14.50 & 14.56 & 14.43 & 14.48 & 14.52 \end{array}$$

Discuss what the data show about change in average global temperatures over time .

The brightness of sunlight at the earth’s surface changes over time depending on whether the earth’s atmosphere is more or less clear. Sunlight dimmed between 1960 and 1990. After 1990, air pollution dropped in industrial countries. Did sunlight brighten? Here are annual averages computed by researchers from data from Ny Alesund, Spitsbergen, Norway, averaging over only clear days each year. (Other locations show similar trends.) The response variable is solar radiation in watts per square meter.

$$\begin{array}{c|cccccccc} \hline \text { Year } & 1993 & 1994 & 1995 & 1996 & 1997 & 1998 & 1999 & 2000 \\ \hline \text { Sun } & 116.0 & 120.0 & 123.0 & 123.5 & 125.5 & 125.0 & 129.0 & 128.0 \\ \hline \end{array}$$

Have average global temperatures been increasing in recent years? Here are the annual average global temperatures for the last 22 years in degrees Celsius:

$$\begin{array}{l|rrrrrrrr} \hline \text { Year } & 1994 & 1995 & 1996 & 1997 & 1998 & 1999 & 2000 & 2001 \\ \text { Temperature } & 14.23 & 14.35 & 14.22 & 14.42 & 14.54 & 14.36 & 14.33 & 14.45 \\ \hline \text { Year } & 2002 & 2003 & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 \\ \text { Temperature } & 14.51 & 14.52 & 14.48 & 14.55 & 14.50 & 14.49 & 14.41 & 14.50 \\ \hline \text { Year } & 2010 & 2011 & 2012 & 2013 & 2014 & 2015 & & \\ \text { Temperature } & 14.56 & 14.43 & 14.48 & 14.52 & 14.59 & 14.80 & & \\ \hline \end{array}$$

Discuss what the data show about changes in average global temperatures over time.

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Choose four numbers that have the largest possible standard deviation.