Section 6.1 Compliant Data

All of the data we have reviewed have “fit” (or come close to fitting) one of these function.

At this point, you will have to choose which the best fit is; it won’t always be obvious.

These are your tools: E – the eyeball test

R value – the larger the value, the better the fit

Common Sense – this is more of a sanity check. Will the model you’ve chosen work for future/past data.

Homework: 4, 7, 8, 10, 13, 15 2. The graph shows how barrel length effects muzzle velocity for a .44 magnum bullet. a) Choose some points off the graph and use regression and the graph of the data to find the best model for the data. b) Briefly defend the equation you chose to model the data. c) Compare the vertex that your equation would specify with the graph (see section 2.3).

Solutions: a) Points selected will vary. Enter the data points into the calculator. (3, 1050), (7, 1350), (8, 1400), (14.5, 1575), (19, 1500), (31, 600), (34, 200)

i) Eyeball Test: Set up STAT PLOT to view the graph: plot1 on, type is scatter plot (upper left), x and y lists should be the names of the lists in which you stored the data. Compare the plot to the compliant data shapes from the text and select the shape(s) that best fit: quadratic.

ii) R-value:

iii) Common Sense: The only shape that could possibly work is the quadratic function. Best equation is b) c)

11. The table shows the natural gas flow in thousands of BTU’s/hour for different pipe lengths and diameters. The longer the pipe the more inhibited the flow of natural gas because of the increase in friction. a) Consider the 1 inch pipe and use regression and the graph of the data to find the best model where the flow is a function of the pipe length. b) Briefly defend the equation you chose to model the data. c) Use your equation to predict the flow rate for 250 feet of pipe. d) Use your equation to find the maximum length of pipe allowable if you need 210,000 BTU’s/hour of gas flow in a 1 inch pipe. Solutions: a) Enter into the calculator the data from the table. i) Eyeball Test: Set up STAT PLOT to view the graph: plot1 on, type is scatter plot (upper left), x and y lists should be the names of the lists in which you stored the data. Compare the plot to the compliant data shapes from the text and select the shape(s) that best fit: power and logarithmic. ii) R-value:

iii) Common Sense: The Power and Logarithmic equations both look good, but the Power better. Best equation: b) Really good visual fit and r- value; makes sense past 300 feet. c) d) Sample Problem 6.1.6

1. Prices for drip coffee at a drive through stand are shown in the table.

a) Use regression and the graph of the data to find the best model for the data. b) Briefly defend the equation you chose to model the data. c) Use your equation to set a price for a 32 ounce coffee, rounded to the nearest quarter.

Solutions: a) Enter into the calculator the data from the table. i) Eyeball Test: Set up STAT PLOT to view the graph: plot1 on, type is scatter plot (upper left), x and y lists should be the names of the lists in which you stored the data. Compare the plot to the compliant data shapes from the text and select the shape(s) that best fit: power and logarithmic.

ii) R-value:

iii) Common Sense: Both look good. Looks like a toss-up. Best equations: and b) They both fit the data, the R-values are both high, and it makes sense at 32oz. c)

A quadratic equation is a great fit too if we are only interested out to 32 ounce; it would be $4.25 for c). Sample Problem 6.1.12

2. The table is used to size home water systems. It shows the feet of head (height of the source above the faucet) that are necessary for different pounds per square inch (PSI) of pressure at the faucet.

a) Use regression and the graph of the data to find the best model where the feet of head is a function of pressure. b) Briefly defend the equation you chose to model the data. c) Use your equation to predict the pressure if there are 60 feet of head. d) Find the slope between 7 and 11 feet and explain its meaning in context.

Solutions: a) Enter into the calculator the data from the table. i) Eyeball Test: Set up STAT PLOT to view the graph: plot1 on, type is scatter plot (upper left), x and y lists should be the names of the lists in which you stored the data. Compare the plot to the compliant data shapes from the text and select the shape(s) that best fit: linear.

ii) R-value:

iii) Common Sense: The Power and Logarithmic equations both look good, but the Power better. Best equation: b) Really good visual fit and r- value. c) d)