| Project 5 - Interpolation of Vehicle Stopping Distances Using
Least Squares Regression |
The following table contains vehicle stopping distances as a function of speed.
|
V (mph) |
D (ft) |
|
0 |
0 |
|
20 |
42 |
|
25 |
56 |
|
30 |
75 |
|
35 |
95 |
|
40 |
116 |
|
45 |
143 |
|
50 |
175 |
|
55 |
210 |
|
60 |
248 |
|
65 |
295 |
|
70 |
343 |
|
75 |
401 |
|
80 |
464 |
A) Use the MATLAB 'polyfit' function to find the equation of the least squares regression line:
D = a0 + a1V
through the data
points.
Display the following results:
- The numerical values of a0 and a1.
- The following sum of squares: SST, SSE, and SSR.
- The coefficient of determination r2 and the correlation coefficient r.
- The standard deviation sy and the standard error of the estimate
sy|x.
B) Fill in the numerical values in the table below.
| i |
Di |
Vi |
Vi2 |
Vi3 |
Vi4 |
ViDi |
Vi2Di |
| 0 |
0 |
|
|
|
|
|
|
| 20 |
42 |
|
|
|
|
|
|
| 25 |
56 |
|
|
|
|
|
|
| 30 |
75 |
|
|
|
|
|
|
| 35 |
95 |
|
|
|
|
|
|
| 40 |
116 |
|
|
|
|
|
|
| 45 |
143 |
|
|
|
|
|
|
| 50 |
175 |
|
|
|
|
|
|
| 55 |
210 |
|
|
|
|
|
|
| 60 |
248 |
|
|
|
|
|
|
| 65 |
295 |
|
|
|
|
|
|
| 70 |
343 |
|
|
|
|
|
|
| 75 |
401 |
|
|
|
|
|
|
| 80 |
464 |
|
|
|
|
|
|
| åVi= |
åDi= |
åVi2= |
åVi3= |
åVi4= |
åViDi= |
åViDi= |
åVi2Di= |
C) In MATLAB, solve the normal equations to find a0, a1, and
a2 in the least squares quadratic:
D = a0 +
a1V + a2V2
through the
data points.
D) Use the MATLAB 'polyfit' function to check your answers for a0, a1,
and a2.
E) Calculate and output SST, SSE, SSR, r2, r, sy,
sy|x.
F) Plot the given data points, the least squares line and the least squares quadratic on the same graph.