1. The following table contains information about the robbery rate (number of robberies per 100,000 population) and percentage of urban population (percentage of people living in urban as opposed to rural areas) across a set of states:

State	Percentage of Urban Population	Robberies per 100,000 People
Massachusetts	91	193
Wisconsin	67	73
South Dakota	28	16
Virginia	72	106
South Carolina	60	99
Texas	81	240
Arizona	75	169
California	96	343
Arkansas	44	88
Hawaii	77	106

Conduct a full regressional analysis using robbery rate as the response variable:

A. Sketch the scatterplot with the least-squares line, and sketch the residual plot. Interpret your sketch. Remember, use robbery rateas the response variable, since that's the value you're trying to predict. (use with calculator)

B. Write and interpret the correlation coefficient.

C. Write the regression equation and interpret the regression coefficient.

D. Show and interpret the coefficient of determination.

E. State whether you think there is a relationship between the two variables, and justify your answer.

F. We know that the percentage of urban population in Idaho is 35%. We also know that the percentage of urban population in Florida is 78%. Predict the robbery rates in each of these states. Are these extrapolations or interpolation, and are they valid predictions?

2. Geothermal power is an important source of energy. Since the amount of energy contained in 1 pound of water is a function of its temperature, you might wonder whether water obtained from deeper wells contains more energy per pound.

Location of Well	Average (max.) Drill Hole Depth (m)	Average (max.) Temperature (C)
El Tateo, Chile	650	230
Ahuachapan, El Salvador	1,000	230
Namafjall, Iceland	1,000	250
Lardarello (region), Italy	600	200
Matsukawa, Japan	1,000	220
Cerro Prieto, Mexico	800	300
Wairakei, New Zealand	800	230
Kizildere, Turkey	700	190
The Geysers, United States	1,500	250

A. Following steps A-E in the previous question, do a full regression analysis, usinghole depth as the explanatory variable.

B. Using the regression equation, predict the temperature of the water in a well with an average drill hole depth of 2000m. Is this a reliable prediction?

3. Use the potency and temperature data below.

An experiment was conducted to observe the effect of an increase in temerature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of these temperatures: 30, 50, 70, and 90. The potency readings observed at each temperature of the experimental period are listed here:

Potency Readings, y	38, 43, 29	32, 26, 33	19, 27, 23	14, 19, 21
Temperature, x	30	50	70	90

A. As before, conduct a full regressional analysis (see 1A-1E) to answer this question:

Within the sample data, is a one-degree increase in storage temperature of antibiotics associated with a decrease in potency? If so, how much?

B. In this case, you'll need to determine which is the response variable in your analysis. Looking at the question, which variable would you say the researcher is more interested in predicting? The predicted variable is the response variable. (You can also look at the research question as an interpretation of a regression coefficientwhen you write a statement that interprets a regression coefficient, which variable goes first?)

4. Below is some hypothetical data that shows the Rating (an index of how many people watch the show) and Average Cost for a 30-second advertisement for a number of game shows:

GAME SHOW	Rating	Average Cost for a 30 Second Ad ($)
Is That Real Hair?	18.2	$55,000
Feng Shui Happy Booth	8.4	$20,000
Love Signals!	13.6	$26,000
How Many Worms?	11.9	$39,000
Spin the Bottle	9.0	$11,000
Wake that Possum!	22.6	$75,000
Sit on a Potato	3.5	$10,000
Name that Fruit!	2.1	$5,000
The $2.00 Question	4.6	$19,000

1. As before, conduct a full (five step) regressional analysis to answer this question:

Within the sample data, is an increase in ratings associated with an increase the average cost for a 30-second ad? If so, how much?

Demographers often examine the relationship between income measures and population factors such as births, deaths, marriages, or migration rates. You have the following data on Per Capita Income in 1987 and the % Births that are "Low Birth Weight" across a sample of states:

STATE	Per Capita Income (as of 1987)	% of Births of "Low Birth Weight"(as of 1988)
Alaska	$13,263	5.0
Colorado	$12,271	7.8
Delaware	$12,785	7.4
Georgia	$11,406	8.4
Iowa	$11,198	5.4
Louisiana	$8,961	8.8
Maine	$10,478	4.8
Minnesota	$12,281	5.0
Nebraska	$11,139	5.5
New York	$13,167	7.8
Ohio	$11,323	6.9
Oregon	$11,045	5.2
South Dakota	$8,910	4.7
Utah	$9,288	5.7
Wisconsin	$11,417	5.4

As before, conduct a full additional analyzes to answer this question within the sample data is an increase in Per Capita income associated with a decrease in the percentage of low birth weights? if so how much? #5