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References

Data from the Centers for Disease Control and Prevention.

Data from the National Center for HIV, STD, and TB Prevention.

Chapter review

The most basic type of association is a linear association. This type of relationship can be defined algebraically by the equations used, numerically with actual or predicted data values, or graphically from a plotted curve. (Lines are classified as straight curves.) Algebraically, a linear equation typically takes the form y = mx + b , where m and b are constants, x is the independent variable, y is the dependent variable. In a statistical context, a linear equation is written in the form y = a + bx , where a and b are the constants. This form is used to help readers distinguish the statistical context from the algebraic context. In the equation y = a + bx , the constant b that multiplies the x variable ( b is called a coefficient) is called as the slope . The slope describes the rate of change between the independent and dependent variables; in other words, the rate of change describes the change that occurs in the dependent variable as the independent variable is changed. In the equation y = a + bx , the constant a is called as the y -intercept. Graphically, the y -intercept is the y coordinate of the point where the graph of the line crosses the y axis. At this point x = 0.

The slope of a line is a value that describes the rate of change between the independent and dependent variables. The slope tells us how the dependent variable ( y ) changes for every one unit increase in the independent ( x ) variable, on average. The y -intercept is used to describe the dependent variable when the independent variable equals zero. Graphically, the slope is represented by three line types in elementary statistics.

Formula review

y = a + bx where a is the y -intercept and b is the slope. The variable x is the independent variable and y is the dependent variable.

Use the following information to answer the next three exercises . A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour.

What are the dependent and independent variables?

dependent variable: fee amount; independent variable: time

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Find the equation that expresses the total fee in terms of the number of hours the equipment is rented.

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Use the following information to answer the next two exercises . A credit card company charges $10 when a payment is late, and $5 a day each day the payment remains unpaid.

Find the equation that expresses the total fee in terms of the number of days the payment is late.

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Is the equation y = 10 + 5 x – 3 x 2 linear? Why or why not?

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Which of the following equations are linear?

a. y = 6 x + 8

b. y + 7 = 3 x

c. y x = 8 x 2

d. 4 y = 8

y = 6 x + 8, 4 y = 8, and y + 7 = 3 x are all linear equations.

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Does the graph show a linear equation? Why or why not?

This is a graph of an equation. The x-axis is labeled in intervals of 1 from -5 to 5; the y-axis is labeled in intervals of 1 from 0 - 8. The equation's graph is a parabola, a u-shaped curve that has a minimum value at (0, 0).
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[link] contains real data for the first two decades of AIDS reporting.

Adults and adolescents only, united states
Year # AIDS cases diagnosed # AIDS deaths
Pre-1981 91 29
1981 319 121
1982 1,170 453
1983 3,076 1,482
1984 6,240 3,466
1985 11,776 6,878
1986 19,032 11,987
1987 28,564 16,162
1988 35,447 20,868
1989 42,674 27,591
1990 48,634 31,335
1991 59,660 36,560
1992 78,530 41,055
1993 78,834 44,730
1994 71,874 49,095
1995 68,505 49,456
1996 59,347 38,510
1997 47,149 20,736
1998 38,393 19,005
1999 25,174 18,454
2000 25,522 17,347
2001 25,643 17,402
2002 26,464 16,371
Total 802,118 489,093

Use the columns "year" and "# AIDS cases diagnosed. Why is “year” the independent variable and “# AIDS cases diagnosed.” the dependent variable (instead of the reverse)?

The number of AIDS cases depends on the year. Therefore, year becomes the independent variable and the number of AIDS cases is the dependent variable.

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Use the following information to answer the next two exercises . A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y = 50 + 100 x .

What are the independent and dependent variables?

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What is the y -intercept and what is the slope? Interpret them using complete sentences.

The y -intercept is 50 ( a = 50). At the start of the cleaning, the company charges a one-time fee of $50 (this is when x = 0). The slope is 100 ( b = 100). For each session, the company charges $100 for each hour they clean.

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Use the following information to answer the next three questions . Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000 x .

What are the independent and dependent variables?

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How many pounds of soil does the shoreline lose in a year?

12,000 pounds of soil

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What is the y -intercept? Interpret its meaning.

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Use the following information to answer the next two exercises . The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is y = 15 – 1.5 x where x is the number of hours passed in an eight-hour day of trading.

What are the slope and y -intercept? Interpret their meaning.

The slope is –1.5 ( b = –1.5). This means the stock is losing value at a rate of $1.50 per hour. The y -intercept is $15 ( a = 15). This means the price of stock before the trading day was $15.

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If you owned this stock, would you want a positive or negative slope? Why?

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Questions & Answers

what is standard deviation?
Jawed Reply
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
Yeah....the simplest one
IRFAN
what is the number of x
Godgift Reply
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
Kingsley Reply
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
adeagbo
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
Kanwal Reply
three coins are tossed consecutively or what ?
umair
p(getting no head)=1/8
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
Umar Reply
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
Anjali Reply
excuse me?
Gabriel
why?
Tade
didn't understand the question though.
Gabriel
which question? ?
Tade
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
geometric mean of two numbers 4 and 16 is:
iphone Reply
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
srijth Reply
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
Eze Reply
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
for poisson distribution mean............variance.
mehul Reply
both are equal to mu
Faizan
mean=variance
Faizan
what is a variable
Bonolo Reply
something that changes
Festus
why we only calculate 4 moment of mean? asked in papers.
Faizan Reply
why we only 4 moment of mean ? asked in BA exam
Faizan
Good evening, can you please help me by sharing regression and correlation analysis notes....thank you in advance
Refiloe Reply
Hello, can you please share the possible questions that are likely to be examined under the topic: regression and correlation analysis.
Refiloe
for normal distribution mean is 2 & variance is 4 find mu 4?
Faizan Reply
repeat quastion again
Yusuf
find mu 4. it can be wrong but want to prove how.
Faizan
for a normal distribution if mu 4 is 12 then find mu 3?
Faizan Reply
Question hi wrong ha
Tahir
ye BA mcqs me aya he teen he. 2dafa aya he
Faizan
if X is normally distributed. (n,b). then its mean deviation is?
Faizan
The answer is zero, because all odd ordered central moments of a normal distribution are Zero.
nikita
which question is zero
Faizan
sorry it is (5,16) in place of (n,b)
Faizan
I got. thanks. it is zero.
Faizan
a random variable having binomial distribution is?
Bokaho

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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