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# Graphs : Regression and Forecasting

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Using the following information answer the following questions.

Year Population
1860 379, 994
1870 560, 247
1880 864, 694
1890 1,213, 398
1900 1,485, 053

A) What is the linear regression function for this data? Write all decimal points.

B) What does the model predict for the year 1880, 1910, 1990?

C) Is the actual population in 1880 the same as the model predicts? Why or Why not?

D)Does the prediction for 1910 seem reasonable and consistent with the population values prior to 1910?
Explain. Defend the explanation by commenting about the differences in the population numbers and analyzing them.

H) In California in 1990 the population was 29, 839, 250. what is the prediction of california's population in the long-run?

I) What factors in life could contribute to the population size in 1990? What things could account for the differences in the predicted value and the actual value?

##### Solution Summary

A graph is analyzed for the purpose of regression and forecasting.

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Using the following information answer the following qustions.

Year population
1860 379, 994
1870 560, 247
1880 864, 694
1890 1213, 398
1900 1485, 053

A) What is the linear regression function for this data? Write all decimal points.
Denote the year by x, and denote the population by y. Then we get
y=28632.7x-52928800

B) what does the model predict for the year 1880, 1910, 1990?
y(1880)=28632.7*1880-52928800=900677
y(1910)=28632.7*1910-52928800=1759657
...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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