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Math 150 Project 1

(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 “2nd STAT PLOT”
ii. Select “1”
iii. Select “On” for Plot 1. Use the arrow keys to move around the
iv. Exit using “2nd 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 “2nd 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
Number of Cans
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

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

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.

(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?