<< Chapter < Page Chapter >> Page >

What would you predict the sales to be on day 60?

$250,120

Got questions? Get instant answers now!

What would you predict the sales to be on day 90?

Got questions? Get instant answers now!


Use the following information to answer the next three exercises . A landscaping company is hired to mow the grass for several large properties. The total area of the properties combined is 1,345 acres. The rate at which one person can mow is as follows:

ŷ = 1350 – 1.2 x where x is the number of hours and ŷ represents the number of acres left to mow.

How many acres will be left to mow after 20 hours of work?

1,326 acres

Got questions? Get instant answers now!

How many acres will be left to mow after 100 hours of work?

Got questions? Get instant answers now!

How many hours will it take to mow all of the lawns? (When is ŷ = 0?)

1,125 hours, or when x = 1,125

Got questions? Get instant answers now!

[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

Graph “year” versus “# AIDS cases diagnosed” (plot the scatter plot). Do not include pre-1981 data.

Got questions? Get instant answers now!

Perform linear regression. What is the linear equation? Round to the nearest whole number.

Check student’s solution.

Got questions? Get instant answers now!

Write the equations:

  1. Linear equation: __________
  2. a = ________
  3. b = ________
  4. r = ________
  5. n = ________

Got questions? Get instant answers now!

Solve.

  1. When x = 1985, ŷ = _____
  2. When x = 1990, ŷ =_____
  3. When x = 1970, ŷ =______ Why doesn’t this answer make sense?

  1. When x = 1985, ŷ = 25,52
  2. When x = 1990, ŷ = 34,275
  3. When x = 1970, ŷ = –725 Why doesn’t this answer make sense? The range of x values was 1981 to 2002; the year 1970 is not in this range. The regression equation does not apply, because predicting for the year 1970 is extrapolation, which requires a different process. Also, a negative number does not make sense in this context, where we are predicting AIDS cases diagnosed.

Got questions? Get instant answers now!

Does the line seem to fit the data? Why or why not?

Got questions? Get instant answers now!

What does the correlation imply about the relationship between time (years) and the number of diagnosed AIDS cases reported in the U.S.?

Also, the correlation r = 0.4526. If r is compared to the value in the 95% Critical Values of the Sample Correlation Coefficient Table, because r >0.423, r is significant, and you would think that the line could be used for prediction. But the scatter plot indicates otherwise.

Got questions? Get instant answers now!

Plot the two given points on the following graph. Then, connect the two points to form the regression line.

Blank graph with horizontal and vertical axes.

Obtain the graph on your calculator or computer.

Got questions? Get instant answers now!

Write the equation: ŷ = ____________

y ^ = 3,448,225 + 1750 x

Got questions? Get instant answers now!

Hand draw a smooth curve on the graph that shows the flow of the data.

Got questions? Get instant answers now!

Does the line seem to fit the data? Why or why not?

There was an increase in AIDS cases diagnosed until 1993. From 1993 through 2002, the number of AIDS cases diagnosed declined each year. It is not appropriate to use a linear regression line to fit to the data.

Got questions? Get instant answers now!

Do you think a linear fit is best? Why or why not?

Got questions? Get instant answers now!

What does the correlation imply about the relationship between time (years) and the number of diagnosed AIDS cases reported in the U.S.?

Since there is no linear association between year and # of AIDS cases diagnosed, it is not appropriate to calculate a linear correlation coefficient. When there is a linear association and it is appropriate to calculate a correlation, we cannot say that one variable “causes” the other variable.

Got questions? Get instant answers now!

Graph “year” vs. “# AIDS cases diagnosed.” Do not include pre-1981. Label both axes with words. Scale both axes.

Got questions? Get instant answers now!

Enter your data into your calculator or computer. The pre-1981 data should not be included. Why is that so?

Write the linear equation, rounding to four decimal places:

We don’t know if the pre-1981 data was collected from a single year. So we don’t have an accurate x value for this figure.

Regression equation: ŷ (#AIDS Cases) = –3,448,225 + 1749.777 (year)

Coefficients
Intercept –3,448,225
X Variable 1 1,749.777
Got questions? Get instant answers now!

Calculate the following:

  1. a = _____
  2. b = _____
  3. correlation = _____
  4. n = _____
Got questions? Get instant answers now!

Questions & Answers

how do you get the 2/50
Abba Reply
number of sport play by 50 student construct discrete data
Aminu Reply
width of the frangebany leaves on how to write a introduction
Theresa Reply
Solve the mean of variance
Veronica Reply
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
kenneth
what is error
Yakuba Reply
Is mistake done to something
Vutshila
Hy
anas
hy
What is the life teble
anas
hy
Jibrin
statistics is the analyzing of data
Tajudeen Reply
what is statics?
Zelalem Reply
how do you calculate mean
Gloria Reply
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
Fisaye Reply
what is statistics
Akhisani Reply
data collected all over the world
Shaynaynay
construct a less than and more than table
Imad Reply
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Aschalew Reply
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
Akshay
1
Bright
Sorry i want to learn more about this question
Bright
Someone help
Bright
a= 0.20233 b=0.3384
Sufiyan
a
Shaynaynay
How do I interpret level of significance?
Mohd Reply
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
Owen Reply
yes what is it
Taneeya

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask