Question 1

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. Round your answers to 3 decimal places

Raspberry Type	grams	Vitamin C content in mg
Farm A - North Field	70	18.5
Farm B - North Field	85	25.5
Farm A - South Field	100	31.4
Farm B - South Field	115	39.1
Farm C -Small Field	130	46
Farm D	145	51.7
Farm E	160	58.4

= -----+-----

Question 2

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express volume as a function of the mass. Round your answers to 3 decimal places

grams	Volume in ml
15	292.7
16.5	325.2
18	344.3
19.5	384.3
21	405.7
22.5	439
24	473

Volume = + where x is the grams of the unknown metal

Question 3

A geologist has gathered the following data from a geophysical study and laboratory experiments to attempt to create a model of a particular are that she was assigned to study. She wants to create a model to determine the pressure-depth. Find a linear model that express degrees Celsius as a function of the Depth. Round your answers to 3 decimal places

Depth (km)	degrees Celsius
0.4	25.9
0.8	41.4
1.2	53.5
1.6	65.3
2	76.2
2.4	86.6
2.8	95

y = x where x is in degrees Centigrade

Question 4

A group of researchers are working to determine the historic sea levels of the body of water. They are attempting to do this by taking samples around the body of water and in a nearby cave and after analyzing sediment cores from around the body of water to those in the cave. The Climatologist that is working in the cave is trying to determine the age and growth rate of stalactites, to get a more accurate picture of the age of the existing stalactites. The following table contains the estimated age (to the nearest thousand) of the sample and the length of the sample in micrometers. Find a linear model that express length as a function of the age. Round your answers to 2 decimal places

Age (nearest thousand)	Micrometers
91	12743
93	13020
96	13433
104	14567
114	15960
116	16224
125	17487

Length = ----+------ where x is the age in thousands of years

Question 5

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries.

grams	Vitamin C content in mg
60	13.9
75	20.5
90	27
105	34.6
120	41
135	48.2
150	54

A) Find the regression equation: =---- +----- Round your answers to 3 decimal places

B) Answer the following questions using your un-rounded regression equation.

If we test 180 grams of raspberries what is the expected Vitamin C content? (round to the nearest tenth)

Question 6

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that expressesvolume as a function of the mass.

grams	Volume in ml
17	174.8
19.5	200.5
22	230.8
24.5	254.4
27	288.9
29.5	303.3
32	332.3

A) Write the linear regression equation for the data in the chart. Volume = ----+ ------where x is the grams of the unknown metal.Round your answers to 3 decimal places

B) If the mass of an unknown metal is 15, using yourun-rounded regression equation find its predicted volume. Round your answer to 1 decimal place. -----

Question 7

number of murders per 100,000 residents for several Northwestern states.

	11.6	8.1	7.1	3.7	2.7	2.2	2.4	0.5
	13.7	10.6	10.3	7.5	6	5.9	6.4	4.7

Use your calculator to do a linear regression expressing the number of murders per 100,000 residents as a function of the number of thousands of state-registered automatic weapons. Also, give the and 2 values from your calculator Regression Equation: = 2 = Round to 3 decimal places. Using your linear regression, how many murders per 100,000 residents can be expected in a state with 7000 automatic weapons? Round to 3 decimal places. Using your linear regression, how many automatic weapons would be expected in a city with 9 murders per 100,000 residents?

Question 8

Gotham City is piloting a crime reduction program so that it does not have to rely on the help of super-heroes anymore. The table below shows the number of crimes committed every year (since 2005). The mayor of Gotham needs your help and you are tasked to find the following:

Years ()	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014
Crimes ()	1370	1342	1336	1324	1326	1314	1330	1310	1302	1311

Use the data to create an appropriate linear function (in equation form) that represents the number of crimes as a function of the calendar year. Also, give the and 2 values from your calculator. Regression Equation: = 2 = Round all values to 3 decimal places. Gotham can stop relying on super-heroes' help once the number of crimes drop below 500 per year. In which year will that happen?

Question 9

Morgan & Smith, a research firm for the real estate industry, studied the relation between = annual income (in thousands of dollars) and = sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table.

Annual Income	House Price
103	244.9
52	88
74	183.6
50	122
73	168.6
72	145.8
62	158.8
79	173.9
105	185.5

Conduct a linear regression. Use the results to answer the following questions.

a. What is the value of the correlation coefficient (round to 3 decimal places)? What does the value tell you about the linear relationship between the annual income and the price of house purchased?

Correlation coefficient:

This indicates:

• very weak negative linear correlation
• fairly strong positive linear correlation
• no linear correlation
• perfect negative linear correlation
• very weak positive linear correlation
• perfect positive linear correlation
• fairly strong negative linear correlation

b. What is the equation of the Least Squares line? Round the parameter values (slope and intercept) to 2 decimal places.

^=

c. If a buyer's annual income increases by $1000, the model's predicted change in DOLLARS of the sale price of the house they will purchase is:

an Select an answer increase decrease of $

(NOTE: be careful of UNITS!)

Question 10

After determining a relationship between cricket chirps and temperature, researchers were curious to see if there was a relationship between rooster crows and temperature. At different temperatures, the number of rooster crows per hour were recorded. These are their findings:

Crows	Temperature
11	61.8
16	69.6
17	75.2
20	88
21	80.4
21	82.4
22	88.2
22	80.6
22	98
22	83

a. Rounded to three decimal places, what is the correlation coefficient for this data? =

Question 11 After determining a relationship between cricket chirps and temperature, researchers were curious to see if there was a relationship between frog ribbits and temperature. At different temperatures, the number of frog ribbits per hour were recorded. These are their findings:

Ribbits	Temperature
11	56.2
15	62
15	66
15	63
16	80
17	65.4
19	73.8
19	82.2
20	76
22	78.6

a. Rounded to three decimal places, what is the correlation coefficient for this data? =

Having found a relationship between the number of ribbits per hour and temperature, statisticians then found a regression model, ^=32.37+2.246, for the data with explanatory variable = ribbits per hour and response variable = temperature (F).

b. Use the given regression line equation to predict the temperature (round to 1 decimal place) if the rate of frog ribbits/hour is 1) 14 ribbits/hour, predicted temp = F 2) 28 ribbits/hour, predicted temp = F

Please, answer the questions sequentially. Thank you.