Name
December 2, 2016
Math 1b/2a
Unit 3: Statistics, Quiz 2 Review
Day 11 Quiz Review: Quantitative Data and Lines of Best Fit
You should be able to:
• Construct scatterplots for quantitative data
• Find lines of best fit for data that is approximately linear (by hand and with Desmos)
• Determine and interpret the correlation coefficient
• Make appropriate predictions based on best-fit lines
• Answer practical questions about data and justify your reasoning
1. For the line graphed to the right:
a. Write the equation of the line in point-slope form using the given point.
b. Convert this equation into slope-intercept form.
2. Convert the following equations into slope-intercept
form and identify the y-intercept.
3
y − 2 = (x − 5)
4
y-intercept = ____________
3. The data is graphed with its line of best fit.
The line goes through the balance point (3, 6) .
Find the equation of the line of best fit.
4. The following is data collected on time spent on homework (min) and time spent watching TV (min)
each night.
Homework
4 40 11 55 23 28 65 39 27 41 44
(min)
Television
(min)
78
15
72
25
40
56
12
50
42
60
34
a. On separate paper, construct a scatterplot for the data.
b. Explain your choices for which variable is on which axis and the scales of each axis.
c. Is there a positive, negative, or no correlation between these variables? Explain what the
relationship means in words.
d. Draw in an appropriate line of best fit on your scatterplot (using the balance point).
e. Write the equation of the best-fit line in point-slope form, using the balance point.
f. Change your point-slope equation into slope-intercept form.
g. Find the line of best fit given by the Desmos information
on the left, rounding to the nearest hundreth. How close is
your line from part e to the one given by Desmos?
h. What is the slope of the line from Desmos? Write a sentence explaining what it represents about
homework and watching television.
i. What is the y-intercept of the line from Desmos? Write a sentence explaining what it represents
about homework and watching television. Does this make sense?
j. Use the Desmos information above to find the correlation coefficient for this data. Explain what it
tells you about the data.
k. Use the equation of the line of best fit to predict how much television was watched if the student
spent 60 minutes on homework.
l. Use the equation of the line of best fit to predict how much homework a student did if they
watched 75 minutes of television.
5.
The following chart shows nutrition information for items at fast food restaurants.
a. Using Desmos or your graphing calculator, generate a scatterplot comparing total calories (x) and
carbohydrates. Estimate the correlation coefficient for theses variables and explain your
reasoning.
b. Determine the equation for the line of best fit and the correlation coefficient from your calculator.
How closely did your estimate match the actual correlation coefficient?
c. A “Bacon Cheeseburger” from Five Guys has 700 calories. Use your line of best fit to predict the
grams of carbohydrates in this burger. Is this an appropriate prediction?
Answers
4a.
4b: Could be either.
4c: negative, More homework – less TV
4d/e: y – 44 = -1 (x – 34.3)
4f: y = -x + 78
4g: y = -.99x + 77.8 (very close)
4h: slope = -.99 (add one hour of homework,
subtract .99 of an hour of TV)
4i: y-intercept = 77.8 (no homework leaves 77.8
minutes for TV)
x=homework, y=television
4j: r = -.82 (correlated, somewhat strongly)
Do Now
1. A scatterplot is graphed at the right. Which of the following equations best fits the data?
A. y = 2x + 3
1
B. y = x + 3
2
C. y = 2x − 3
D. y = −2x + 3
2. Alex had the following data graphed at the right. The then typed in the equation to find line of best fit.
d. What is the equation of the line of best fit?
e. What is the correlation coefficient?
f. Explain what the correlation coefficient means for the data.