MATH 225N WEEK 8 QUESTIONS & 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
y
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 2:
Well done! You got it right.
y = 2.89, x 4.69
, Thus, the equation of line of best fit with slope and intercept rounded to two
decimal places is yˆ=2.86x+4.69.
In the following table, the age (in years) of the respondents is given as the x value,
and the earnings (in thousands of dollars) of the respondents are given as
the y value. Use Excel to find the best fit linear regression equation in thousands of
dollars. Round the slope and intercept to three decimal places.
Yes that's right. Keep it up!
y = 0.433, x=24.493
Answer Explanation
Thus, the equation of line of best fit with slope and intercept rounded to three
decimal places is yˆ=0.433x+24.493.
PREDICITONS USING LINEAR REGRESSION
Question
The table shows data collected on the relationship between the time spent studying
per day and the time spent reading per day. The line of best fit for the data
is yˆ=0.16x+36.2. Assume the line of best fit is significant and there is a strong
linear relationship between the variables.
Studying (Minutes) 507090110 Reading (Minutes) 44485054
(a) According to the line of best fit, what would be the predicted number of
minutes spent reading for someone who spent 67 minutes studying? Round your
answer to two decimal places.
Yes that's right. Keep it up!
The predicted number of minutes spent reading is $$46.92.
Answer Explanation
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
y
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 2:
Well done! You got it right.
y = 2.89, x 4.69
, Thus, the equation of line of best fit with slope and intercept rounded to two
decimal places is yˆ=2.86x+4.69.
In the following table, the age (in years) of the respondents is given as the x value,
and the earnings (in thousands of dollars) of the respondents are given as
the y value. Use Excel to find the best fit linear regression equation in thousands of
dollars. Round the slope and intercept to three decimal places.
Yes that's right. Keep it up!
y = 0.433, x=24.493
Answer Explanation
Thus, the equation of line of best fit with slope and intercept rounded to three
decimal places is yˆ=0.433x+24.493.
PREDICITONS USING LINEAR REGRESSION
Question
The table shows data collected on the relationship between the time spent studying
per day and the time spent reading per day. The line of best fit for the data
is yˆ=0.16x+36.2. Assume the line of best fit is significant and there is a strong
linear relationship between the variables.
Studying (Minutes) 507090110 Reading (Minutes) 44485054
(a) According to the line of best fit, what would be the predicted number of
minutes spent reading for someone who spent 67 minutes studying? Round your
answer to two decimal places.
Yes that's right. Keep it up!
The predicted number of minutes spent reading is $$46.92.
Answer Explanation
