math 225n week 8 final exam math225 week 8 final exam version 1
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MATH225 Week 8 Final Exam
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
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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.
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.
(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 $$46.92.
Answer Explanation
The predicted number of minutes spent reading is 1$$.
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