(20 points)

Regression and Modeling by Linear, Quadratic and Cubic Equations

1. Read the Yellow Sections at the end of Chapter 2 and the end of Chapter 3.

2. We will go over in class how to use your calculator (TI-83) to do the
following:

a. Input data points

i. Hit the “STAT” button

ii. Select “EDIT”

iii. Type in the x-values in the column L1

iv. Type in the y-values in the column L2

v. You can use the “DEL” button to delete entries.

b. Plot a scatter plot of the data

i. Hit “2^{nd} STAT PLOT”

ii. Select “1”

iii. Select “On” for Plot 1. Use the arrow keys to move around the

screen.

iv. Exit using “2^{nd} QUIT”

v. Change the Viewing Window to fit you data values

vi. Hit “GRAPH”

c. Find a regression equation (linear, quadratic or cubic,
etc)

i. Hit “STAT”

ii. Move the cursor to “CALC” on the top line

iii. Select the type of Regression you want (4 – C)

iv. The Result are the parameters of the “Best Fit” curve of that type.

d. Plot the data along with the regression equation.

i. Hit “Y=” button

ii. Move to the equation you want to enter (i.e. Y1= )

iii. Hit “VARS”

iv. Select “STATISTICS”

v. Move with the arrows to EQ (for equations)

vi. Select “RegEQ”

vii. This puts the equation in Y1=…

viii. Finally, Hit “GRAPH” to see you data points and the graph together.

e. To use the Regression Equation to Predict a y-value.

i. Either trace along the regression curve, or

ii. Hit “2^{nd} CALC”

iii. Hit “1: Value” and enter the x-value.

3. Solve the following problems

Page 243 # 2.

A convenience store owner notices that sales of soft
drinks are higher on hotter days,

so he assembles the data in the following table.

a. Make a scatter plot of the data. Draw it to the right of the table.

High Temp in Fahrenheit |
Number of Cans Sold |

55 | 340 |

58 | 335 |

64 | 410 |

68 | 460 |

70 | 450 |

75 | 610 |

80 | 735 |

84 | 780 |

b. Find and graph a linear function that models the data.

y =

c. Use the model to predict the number of soft drinks sold
if the temperature were 95

degrees.

d. How many drinks would be sold if the temperature were 30 degrees?

Page 244 # 4

The table list the average carbon dioxide levels in the
atmosphere, measured in parts

per million from 1984 until 2000.

a. Make a scatter plot of the data.

Year | CO2 Level (ppm) |

1984 | 344.3 |

1986 | 347.0 |

1988 | 351.3 |

1990 | 354.0 |

1992 | 356.3 |

1994 | 358.9 |

1996 | 362.7 |

1998 | 366.5 |

2000 | 369.4 |

b. Find and graph the regression line.

y =

c. Use the linear model to estimate the amount of CO2 in
the atmosphere in 2007

and in 2050.

d. After you do that suppose you knew that the actual
value in 2006 was 385.7.

Find a new regression line for that data. How does your prediction for 2050

change?

Page 323 # 2

The more corn a farmer plants per acre the greater the
yield that he can expect, but

only up to a point. Too many plants per acre can cause overcrowding and decrease
the

overall yield. The data give the crop yields per acre for various densities of
corn.

a. Draw a scatter plot of the data.

Density (Thousand plants / acre) |
Crop Yield (bushels/acre) |

15 | 43 |

20 | 98 |

25 | 118 |

30 | 140 |

35 | 142 |

40 | 122 |

45 | 93 |

50 | 67 |

b. Draw a graph of the quadratic equation that best models
the data.

y =

c. Use your quadratic equation to model the yield for 37,000 plants per acre.

d. What density do you predict will give the maximum yield?

Page 324 # 6

Water in a tank will flow out of a small hole in the
bottom faster when the tank is

nearly full than when it is nearly empty. According to Torrelli’s Law, the
height ‘h(t)’

of water remaining at time ‘t’ is a quadratic function of ‘t’. A certain tank is
filled

with water and allowed to drain out. The height of the water at different times
is

measured and shown in the table.

a. Plot the data on a scatter plot.

Time (minutes) | Height (feet) |

0 | 5.0 |

4 | 3.1 |

8 | 1.9 |

12 | 0.8 |

16 | 0.2 |

b. Find the quadratic function that best fits the data.

y =

c. Draw the graph of the equation on the scatter plot.

d. According to your equation, how long will it take to
drain completely?

According to your equation, what happens after that?