Performing Linear Regressions with Technology
An amateur astronomer is researching statistical properties of known stars using avariety of
databases.
... [Show More] They collect the absolute magnitude or MV and stellar mass
or M⊙ for 30 stars. The absolute volume of a star is the intensity of light that wouldbe
observed from the star at a distance of 10 parsecs. 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. Thedata is
provided below. Use Excel to calculate the correlation coefficient r between the
two data sets, rounding to two decimal places.
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 recordedthe
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.
Answer Explanation
r= −0.81
Yes that's right. Keep it up!
Correct! You nailed it.
r= −0.93
2
The correlation coefficient, rounded to two decimal places, is r≈−0.81.
3
The table below contains the geographic latitudes, x, and average Januarytemperatures, y, of
20cities. Use Excel to find the best fit linear regression
equation. Round the slope and intercept to two decimal places.
46
23
32
60
39
40
33
59
38
57
40
33
42
33
30
64
34
56
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y = −2.68, x147.24
Thus, the equation of line of best fit with slope and intercept rounded to twodecimal
places is yˆ=−2.68x+147.24.
An organization collects information on the life expectancy (in years) of a person incertain
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 Explanation yˆ=−4.21, x+83.68.
x
y
Yes that's right. Keep it up!
4
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 ratioand
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.
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.
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 explanatoryvariable.
Round the slope and intercept to two decimal places.
Answer 1:
y = 0.35, x28.99
Answer 2:
Great work! That's correct.
r= 0.50
r= −0.17
Perfect. Your hard work is paying off
That's not right - let's review the answer.
Well done! You got it right.
5
Yes that's right. Keep it up!
y = 2.89, x 4.69
Thus, the equation of line of best fit with slope and intercept rounded to twodecimal
places is yˆ=2.86x+4.69.
In the following table, the age (in years) of the respondents is given as the x value, andthe
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 theslope
and intercept to three decimal places.
y = 0.433, x=24.493
Answer Explanation
Thus, the equation of line of best fit with slope and intercept rounded to threedecimal
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 perday 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.
The predicted number of minutes spent reading is $$46.92.
Yes that's right. Keep it up!
6
Answer Explanation
The predicted number of minutes spent reading is 1$$.
Correct answers:
Substitute 67 for x into the line of best fit to estimate the number of minutes spent reading for
someone who spent 67 minutes
studying: yˆ=0.16(67)+36.2=46.92. [Show Less]