Which choices BEST describes the relationship between the variables shown in the graph below?
A scatter plot is shown with 20 data points showing a strong positive relationship. The x-values of the data points extend from 0 to 9, and the y-values of the data points extend from 80 to 10.
a
People who completed more years of college generally made less money than those who completed fewer years of college.
b
Going to college CAUSES a person to earn more income.
c
People who made more money generally completed more years of college than those who made less money.
d
There is a strong, positive correlation between years of college and income.
e
There is no relationship between college completion and income.
f
People should go to college.
d (There is a strong, positive correlation between years of college and income.)
5.1 Scatter Plots | STM1001 Topic 2 - Descriptive Statistics
Check all of the statements that are true. (hint: there are 3!)
a
This is a moderate positive correlation
b
The line of best fit should have the same number of points above and below it
c
The line of best fit must pass through at least 2 points on the scatter plot
d
The slope of the line of best fit could be around - 1/2000
e
As a person's income goes up, their happiness trends down.
f
There is no correlation between happiness and income.
g
The line of best fit would have a positive slope.
h
The y-intercept of the line of best fit would be around 45.
a, d, g (This is a moderate positive correlation; The slope of the line of best fit could be around - 1/2000; The line of best fit would have a positive slope.)
The lesson length (in minutes) and the cost (in dollars) of piano lessons given by nine different piano instructors are shown in the table below.
The table shows 30 minutes lesson costs 45 dollars by the first instructor, 30 minutes lesson costs 25 dollars by the second instructor, 45 minutes lesson costs 60 dollars by the third instructor, 20 minutes lesson costs 35 dollars by the fourth instructor, 60 minutes lesson costs 50 dollars by the fifth instructor, 50 minutes lesson costs 55 dollars by the sixth instructor, 60 minutes lesson costs 75 dollars by the seventh instructor, 30 minutes lesson costs 50 dollars by the eighth instructor, and 60 minutes lesson costs 80 dollars by the ninth instructor.
Which of the following scatter plots correctly displays this data?
a
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 35), (30, 25), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), and (60, 80).
b
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (25, 30), (35, 20), (45, 30), (50, 30), (50, 60), (55, 50), (60, 45), (75, 60), and (80, 60).
c
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 25), (30, 35), (30, 45), (30, 50), (45, 50), (50, 55), (60, 60), (60, 75), and (60, 80).
d
A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 35), (25, 30), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), and (60, 80).
d (A scatter plot on graph titled 'piano lessons' showing 'lesson length in minutes' from 0 to 80 along the x-axis and 'lesson cost in dollars' from 0 to 80 along the y-axis, is shown with 9 data points at (20, 35), (25, 30), (30, 45), (30, 50), (45, 60), (50, 55), (60, 50), (60, 75), and (60, 80).)
The manager of a company made the graph below to show the value of a piece of office equipment after each of the 7 years following its purchase.
The graph titled value of equipment shows value on y-axis and time on x-axis. There are dots at (1, 7), (2, 6.5), (3, 6.4), (4, 4), (5, 2.5), (6, 2), and (7, 0.5).
Match the statement with the correct answer
Column A
1.
The slope of the line of best fit:
The slope of the line of best fit
2.
The y-intercept of the line of best fit:
The y-intercept of the line of best fit
3.
The graph of the line of best fit:
The graph of the line of best fit
4.
The correlation of the line of best fit:
The correlation of the line of best fit
5.
The equation for the line of best fit.:
The equation for the line of best fit.
Column B
a. -1
b. y = 8x - 1
c. y = -8x + 1
d. +1
e. y = -x + 8
f. 5
g. Weak, positive trend
h. Strong, negative trend
1. c (y = -8x + 1)
2. e (y = -x + 8)
3. f (5)
4. g (Weak, positive trend)
5. b (y = 8x - 1)
The scatter plot on graph showing the points (1, 7), (2, 6), (3, 5), (4, 3), (5, 4), (6, 2), (6, 3), (7, 3), (8, 1), and (8, 2).
Which linear equation would best fit the data points plotted?
a
\large y=-1x+7.5
b
\large y=1x+7.5
c
\large y=-7.5x+1
d
\large y=7.5x+1
c (y = -7.5x + 1)
The manager of a company made the graph below to show the value of a piece of office equipment after each of the 7 years following its purchase.
The graph titled value of equipment shows value on y-axis and time on x-axis. There are dots at (1, 7), (2, 6.5), (3, 6.4), (4, 4), (5, 2.5), (6, 2), and (7, 0.5).
Match the statement with the correct answer
Column A
1.
The slope of the line of best fit:
The slope of the line of best fit
2.
The y-intercept of the line of best fit:
The y-intercept of the line of best fit
3.
The graph of the line of best fit:
The graph of the line of best fit
4.
The correlation of the line of best fit:
The correlation of the line of best fit
5.
The equation for the line of best fit.:
The equation for the line of best fit.
Column B
Column B
a.
The scatter plot titled value of equipment shows value in thousands of dollars from 0 to 10 and time in years from 0 to 10. The points on the scatter plot are (1, 7), (2, 6.5), (4, 4), (5, 2.5), (6, 2), (7, 0.5)
b. y = -8x + 1
c. (0,8)
d. 5
e. Weak, positive trend
f. Strong, negative trend
g.
h. y = -x + 8
i. y = 8x + 1
j. Strong, positive trend
k. +1
l. Weak, negative trend
m. -1
n. y = x + 8
o. y = 8x - 1