MATH 225N WEEK 8 QUESTIONS WITH ANSWERS
Performing Linear Regressions with Technology
An amateur astronomer is researching statistical properties of known stars
using a variety of databases. They collect the absolute magnitude or MV
and stellar mass
or M⊙ for 30 stars. The absolute magnitude of a star is the intensity of
light that would be observed from the star at a distance of 10 parsecs from
the star. This is measured
in terms of a particular band of the light spectrum, indicated by the
subscript letter, which in this case is V for the visual light spectrum. The
scale is logarithmic and
an MV that is 1 less than another comes from a star that is 10 times more
luminous
than the other. The stellar mass of a star is how many times the sun's mass
it has. The data is provided below. Use Excel to calculate the correlation
coefficient r between the
two data sets, rounding to two decimal places.
Correct! You nailed it.
r= −0.93
Answer Explanation
The correlation coefficient, rounded to two decimal places, is r≈−0.93.
A market researcher looked at the quarterly sales revenue for a large e-commerce
store
and for a large brick-and-mortar retailer over the same period. The
researcher recorded the revenue in millions of dollars for 30 quarters. The
data are provided below. Use Excel to calculate the correlation coefficient r
between the two data sets. Round your
answer to two decimal places.
, Yes that's right. Keep it up!
r= −0.81
Answer Explanation
The correlation coefficient, rounded to two decimal places, is r≈−0.81.
,The table below contains the geographic latitudes, x, and average January
temperatures, y, of 20cities. Use Excel to find the best fit linear regression
equation. Round the slope and intercept to two decimal places.
x
46
23
32
60
39
40
33
59
38
57
40
33
42
33
30
64
34
56
HelpCopy to ClipboardDownload CSV
Yes that's right. Keep it up!
y = −2.68, x147.24
Thus, the equation of line of best fit with slope and intercept rounded
to two decimal places is yˆ=−2.68x+147.24.
An organization collects information on the life expectancy (in years) of a
person in certain countries and the fertility rate per woman in those
countries. The data
for 21 randomly selected countries for the year 2011 is given below. Use Excel
to
find the best fit linear regression equation, where fertility rate is the
explanatory variable. Round the slope and intercept to two decimal
places.
y = −4.21, x 83.68 Answer Explanationyˆ=−4.21, x+83.68.
, An economist is trying to understand whether there is a strong link between CEO
pay
ratio and corporate revenue. The economist gathered data including the
CEO pay ratio and corporate revenue for 30 companies for a particular
year. The pay ratio data is
reported by the companies and represents the ratio of CEO compensation to the
median employee salary. The data are provided below. Use Excel to
calculate the correlation coefficient r between the two data sets. Round
your answer to two decimal
places.
Perfect. Your hard work is paying off
r= −0.17
The correlation coefficient, rounded to two decimal places, is r≈−0.17.
A researcher is interested in whether the variation in the size of human
beings is proportional throughout each part of the human. To partly answer
this question they
looked at the correlation between the foot length (in millimeters) and height
(in centimeters) of 30 randomly selected adult males. The data is provided
below. Use Excel to calculate the correlation coefficient r between the two
data sets. Round your
answer to two decimal places.
Great work! That's correct.
r= 0.50
The correlation coefficient, rounded to two decimal places, is r≈0.50.
The table below gives the average weight (in kilograms) of certain people ages 1–
20.
Use Excel to find the best fit linear regression equation, where age is the
explanatory variable. Round the slope and intercept to two decimal places.
Answer 1:
That's not right - let's review the answer.
y = 0.35, x28.99
Answer 2:
Well done! You got it right.
Performing Linear Regressions with Technology
An amateur astronomer is researching statistical properties of known stars
using a variety of databases. They collect the absolute magnitude or MV
and stellar mass
or M⊙ for 30 stars. The absolute magnitude of a star is the intensity of
light that would be observed from the star at a distance of 10 parsecs from
the star. This is measured
in terms of a particular band of the light spectrum, indicated by the
subscript letter, which in this case is V for the visual light spectrum. The
scale is logarithmic and
an MV that is 1 less than another comes from a star that is 10 times more
luminous
than the other. The stellar mass of a star is how many times the sun's mass
it has. The data is provided below. Use Excel to calculate the correlation
coefficient r between the
two data sets, rounding to two decimal places.
Correct! You nailed it.
r= −0.93
Answer Explanation
The correlation coefficient, rounded to two decimal places, is r≈−0.93.
A market researcher looked at the quarterly sales revenue for a large e-commerce
store
and for a large brick-and-mortar retailer over the same period. The
researcher recorded the revenue in millions of dollars for 30 quarters. The
data are provided below. Use Excel to calculate the correlation coefficient r
between the two data sets. Round your
answer to two decimal places.
, Yes that's right. Keep it up!
r= −0.81
Answer Explanation
The correlation coefficient, rounded to two decimal places, is r≈−0.81.
,The table below contains the geographic latitudes, x, and average January
temperatures, y, of 20cities. Use Excel to find the best fit linear regression
equation. Round the slope and intercept to two decimal places.
x
46
23
32
60
39
40
33
59
38
57
40
33
42
33
30
64
34
56
HelpCopy to ClipboardDownload CSV
Yes that's right. Keep it up!
y = −2.68, x147.24
Thus, the equation of line of best fit with slope and intercept rounded
to two decimal places is yˆ=−2.68x+147.24.
An organization collects information on the life expectancy (in years) of a
person in certain countries and the fertility rate per woman in those
countries. The data
for 21 randomly selected countries for the year 2011 is given below. Use Excel
to
find the best fit linear regression equation, where fertility rate is the
explanatory variable. Round the slope and intercept to two decimal
places.
y = −4.21, x 83.68 Answer Explanationyˆ=−4.21, x+83.68.
, An economist is trying to understand whether there is a strong link between CEO
pay
ratio and corporate revenue. The economist gathered data including the
CEO pay ratio and corporate revenue for 30 companies for a particular
year. The pay ratio data is
reported by the companies and represents the ratio of CEO compensation to the
median employee salary. The data are provided below. Use Excel to
calculate the correlation coefficient r between the two data sets. Round
your answer to two decimal
places.
Perfect. Your hard work is paying off
r= −0.17
The correlation coefficient, rounded to two decimal places, is r≈−0.17.
A researcher is interested in whether the variation in the size of human
beings is proportional throughout each part of the human. To partly answer
this question they
looked at the correlation between the foot length (in millimeters) and height
(in centimeters) of 30 randomly selected adult males. The data is provided
below. Use Excel to calculate the correlation coefficient r between the two
data sets. Round your
answer to two decimal places.
Great work! That's correct.
r= 0.50
The correlation coefficient, rounded to two decimal places, is r≈0.50.
The table below gives the average weight (in kilograms) of certain people ages 1–
20.
Use Excel to find the best fit linear regression equation, where age is the
explanatory variable. Round the slope and intercept to two decimal places.
Answer 1:
That's not right - let's review the answer.
y = 0.35, x28.99
Answer 2:
Well done! You got it right.
