I have this graph with the numbers
Year population (thousands)
1950 132
1960 187
1970 254
1980 346
1990 466
2000 657
I need help in analyzing this data so that I can determine the year in which the population will reach 1,000,000 people. how would i make at least two estimates using different regression models.
Thank you so much i would really appreciate it if you could help me
You could use a least-squares linear fit, quadratic fit, or exponential fit. I'd favor the later. An easy way to do it would be by doing a linear fit of the log of the population.
Year Pop Log Pop
1950 132 2.12
1960 187 2.27
1970 254 2.40
1980 346 2.54
1990 466 2.67
2000 657 2.82
Note that the log(base 10)of the population changes by an average of 0.14 per decade
That is easily extrapolated to:
2010 (912) 2.96
2013 1000 3.00
as a Geometric Sequence, r=1.4
GROWTH FORMULA
C=Co(1+(r/100))^n
C=population you want to find(1 million)
Co=initial population (132 thousands)
r=1.4 so r/100=0.014 ,n is No. years
Hence,
1,000=132(1.014)^n
1.014^n=1000/132
n= log(100/132)/log1.014
and then you ll find a value, let's say x
you add x+1950=and get the year
I think it's right..you can work it out and post whether it worked or not.
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To estimate the year in which the population will reach 1,000,000 people using regression models, you can try two different approaches: linear regression and exponential regression.
1. Linear Regression:
Linear regression assumes a linear relationship between the population and the year. To use linear regression, you need to plot the data points on a graph and fit a straight line that best represents the trend.
Here's how you can perform linear regression:
1. Plot the data points on a scatter plot, with the year on the x-axis and the population on the y-axis.
2. Use a regression calculator or software to calculate the equation of the line that best fits the data points. The equation will be in the form of y = mx + c, where y is the population, x is the year, m is the slope, and c is the y-intercept.
3. Utilize the equation to estimate the year when the population will reach 1,000,000. Simply set y = 1,000,000 and solve for x.
2. Exponential Regression:
Exponential regression assumes an exponential growth pattern between the population and the year. This model is more suitable when the population growth rate increases over time.
Here's how you can perform exponential regression:
1. Take the natural logarithm of the population values.
2. Plot these natural logarithm values against the year.
3. Use a regression calculator or software to calculate the equation of the exponential curve that best fits the data points. The equation will be in the form of y = ae^(bx), where y is the natural logarithm of the population, x is the year, a is a constant, and b is the growth rate parameter.
4. Utilize the equation to estimate the year when the population will reach 1,000,000. Apply the inverse natural logarithm function to both sides of the equation and solve for x.
By using both linear and exponential regression, you can make at least two estimates for the year when the population will reach 1,000,000 people based on the given data.