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

$250,120

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

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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

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

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

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

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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

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

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

Check student’s solution.

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Write the equations:

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

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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.

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

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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.

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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.

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Write the equation: ŷ = ____________

y ^ = 3,448,225 + 1750 x

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

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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.

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

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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.

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

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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
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Calculate the following:

  1. a = _____
  2. b = _____
  3. correlation = _____
  4. n = _____
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Questions & Answers

Two dice are thrown. Let A be the event that the sum of the upper face number is odd and be the event of at least one ace
Sana Reply
does proportion alwaus give u a yes or no answer for data
Adrienne Reply
frequency destribution
the Reply
प्रायिकता सिध्दान्त पर आधारित प्रतिदर्श सिध्दान्त का विकास किसने किया?
Lokesh Reply
7.The following data give thenumber of car thefts that occurred in a city in the past 12 days. 63711438726915 Calculate therange, variance, and standard deviation.
Mitu Reply
express the confidence interval 81.4% ~8.5% in interval form
Xx Reply
a bad contain 3 red and 5 black balls another 4 red and 7 black balls, A ball is drawn from a bag selected at random, Find the probability that A is red?
Shazain Reply
The information is given as, 30% of customers shopping at SHOPNO will switch to DAILY SHOPPING every month on the other hand 40% of customers shopping at DAILY SHOPPING will switch to other every month. What is the probability that customers will switch from A to B for next two months?
sharmin Reply
Calculate correlation coefficient, where SP(xy) = 144; SS(x) = 739; SS(y) = 58. (2 Points)
Ashfat Reply
The information are given from a randomly selected sample of age of COVID-19 patients who have already survived. These information are collected from 200 persons. The summarized information are as, n= 20; ∑x = 490; s^2 = 40. Calculate 95% confident interval of mean age.
Ashfat
The mode of the density of power of signal is 3.5. Find the probability that the density of a random signal will be more than 2.5.
Ashfat
The average time needed to repair a mobile phone set is 2 hours. If a customer is in queue for half an hour, what is the probability that his set will be repaired within 1.6 hours?
Ashfat
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 9 and variance 0.04. Do you think that the mean thickness of the spearmint gum it produces is 8.4
nazrul Reply
3. The following are the number of mails received in different days by different organizations: Days (x) : 23, 35, 38, 50, 34, 60, 41, 32, 53, 67. Number of mails (y) : 18, 40, 52, 45, 32, 55, 50, 48, 26, 25. i) Fit a regression line of y on x and test the significance of regression. ii) Estimate y
Atowar Reply
The number of problem creating computers of two laboratories are as follows: Number of computers: 48, 6, 10, 12, 30, 11, 49, 17, 10, 14, 38, 25, 15, 19, 40, 12. Number of computers: 12, 10, 26, 11, 42, 11, 13, 12, 18, 5, 14, 38. Are the two laboratories similar in respect of problem creating compute
Tamim Reply
Is the severity of the drug problem in high school the same for boys and girls? 85 boys and 70 girls were questioned and 34 of the boys and 14 of the girls admitted to having tried some sort of drug. What can be concluded at the 0.05 level?
Ashfat Reply
null rejected
Pratik
a quality control specialist took a random sample of n=10 pieces of gum and measured their thickness and found the mean 7.6 and standered deviation 0.10. Do you think that the mean thickness of the spearmint gum it produces is 7.5?
Shanto Reply
99. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct? a
Niaz Reply
A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct?
Niaz
what is null Hypothesis
Niaz
what is null Hypothesis
Niaz

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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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