MATH 225N WEEK 8 FINAL EXAM 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.

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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.

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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

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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)507090110Reading(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

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