Need help in Statisitcs

Question

The following table shows the percentage of children in a certain country between the ages of 3 and 5 who are enrolled in preprimary programs.

Date	2008	2010	2012	2014
Percentage	65.0	65.3	66.1	66.7

Use extrapolation to estimate the percentage of children enrolled in 2016. (Round your answer to one decimal place.)

Answer 1

The answer can be found with a linear regression. But first, a word of caution: in the real world, it's always dangerous to extrapolate from past data to predict the future. As you probably know, trying to extrapolate stock market values can be risky, unreliable, and even end up a totally wrong prediction.

Still, for this problem, I used Stat Plot in my TI-83 graphing calculator to graph the data, putting 0 for the year 2008 and 6 for year 2014. Then, I did Linreg and found, for the equation y = ax + b:

a = .295

b = 64.89

r = .9868

Therefore, when x = 8, for year 2016:

y = (.295)(8) + 64.89 = 67.25

The estimate for the year 2016 is 67.3%

Answer 2

Hello, Nay!

Well... You can plot 'Date' vs 'Percentage' and see the linear relationship. So, you could apply a simple linear regression on these data with Percentage_hat = ∝ + ß*Date.

Applying the formulas presented in https://en.wikipedia.org/wiki/Simple_linear_regression you will find something about: Percentage_hat = -527.470 + 0.295*Date

Finally, you will get 67.2 when plug 2016 in 'Date'.

See you!!