M143 Week 3 Worksheet
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Boise State University *
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Course
143
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by ChancellorDovePerson1020
M143 Week 3 Worksheet
Math 143 Week 3 Worksheet
Directions: Answer all questions. Show all work. Ask for help if you need it. Due: Thursday, September 7th at 11:59 PM
1.
What are the characteristics of linear data?
Linear data has an approximately constant rate of change. If you calculate the rate of change between any two of points in the data set, you will get around the same value each time. It probably won’t be exactly the same because data usually has some error (called noise) and a linear model might not perfectly describe what’s happening with the data.
2.
What is a line of best fit?
The equation of a line that best describes the relationship between variables according to some goodness-of-fit criteria.
3.
When plotting data, how do you determine which values should be represented by the vertical axis and which should be represented by the horizontal axis
The horizontal axis has the independent variable which is a quantity being manipulated in an experiment. It’s the thing you have control over. The vertical
axis has the dependent variable which is a quantity whose value depends on how the independent variable is manipulated. It’s the outcome.
4.
Find the equation of the line with slope -2/3 that passes through the point (-1, 6). Show your work. Give exact answers, not decimal approximations
6 = -⅔ (-1) +b
6 = ⅔ +b
20/3 = b
y = -2/3x + 20/3
5.
Answer parts a through g for the data set below. A student is hanging weights from a spring and measuring the resulting stretch in the spring. The following table shows the student’s collected data. w (grams)
3
7
9
16
24
s (cm)
15.3
21.0
25.1
33.4
43.2
a)
Which is the independent variable and which is the dependent variable?
The independent variable is the amount of weight and the dependent variable is
the total stretch.
b)
Give the domain and range of this data set.
Domain: {3, 7, 9, 16, 24}
Range: {15.3, 21.0, 25.1, 33.4, 43.2}
c)
Make a scatter plot of this data in Desmos. Include a sketch or screenshot of the
scatterplot below. Make sure your axes are labeled as “weight” and “stretch”
d)
What window did you use to display the data? Explain why you chose this window.
The window for x is between -10 and 60 and y is between 0 and 50. I choose a window that shows all of the data, but doesn’t make them too squished up.
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e)
Calculate a linear regression for this data. Write the regression equation below. Look at the last slide in the week 3 module or ask for help in class if you aren’t sure how to do this
y = 1.31587x + 12.0728
f)
Explain how you can use this regression equation.
You can use this regression equation because you can predict how much stretch
x cm in the spring after the weights were added.
g)
How far would the spring stretch if the mass was 20 g? Show your work.
y = 1.31587(20) + 12.0728
y = 26.3174 + 12.0728
y = 38.3902 cm