Answer the following Question :
(a) Plot the data as discrete points (e.g., circles).
b) Use the polynomial tting function from your software system (e.g., polyfit in MATLAB) to nd the interpolating polynomial through all the given data points and evaluate it for each year from 1780 to 1960.
Plot this curve on the same gure as the circles above and manually change the y-axis limits to [-50; 200]. (Hint: ylim([0, 200]).) Is this a good t to the data? What is going wrong? Why?
(c) Rather than use a polynomial, repeat part (b) using a cubic spline interpolant. (You may use the built-in function for computing splines in your software system, e.g., spline in MATLAB.) Does this give better results that above?
| year |
population |
| 1790 |
3.929 |
| 1800 |
5.038 |
| 1810 |
7.240 |
| 1820 |
9.638 |
| 1830 |
12.866 |
| 1840 |
17.069 |
| 1850 |
23.192 |
| 1860 |
31.433 |
| 180 |
38.558 |
| 1880 |
50.156 |
| 1890 |
62.948 |
| 1900 |
75.996 |
| 1910 |
91.972 |
| 1920 |
105.711 |
| 1930 |
122.775 |
| 1940 |
131.669 |
| 1950 |
150.697 |