Question

1. Experiments with a periodic process gave the following data: $t$: 0 50 100 150 200 250 300 350 $y$: 0.754 1.762 2.041 1.412 0.303 -0.484 -0.380 0.520 Estimate the parameters $c_0$ and $c_1$ in the model $y = c_1 + c_0 sin(t)$, using least square approximation.

Name: 1 experiments with a periodic process gave the following data t 0 50 100 150 200 250 300 350 y 0754 1762 2041 1412 0303 0484 0380 0520 estimate the parameters c0 and c1 in the model y c1 49567
Uploaded: 2023-04-18T14:24:00-08:00
Duration: 3 min 8 s
Channel: Madhur L
Description: 1 experiments with a periodic process gave the following data t 0 50 100 150 200 250 300 350 y 0754 1762 2041 1412 0303 0484 0380 0520 estimate the parameters c0 and c1 in the model y c1 49567

          1. Experiments with a periodic process gave the following data:
$t$: 0 50 100 150 200 250 300 350
$y$: 0.754 1.762 2.041 1.412 0.303 -0.484 -0.380 0.520
Estimate the parameters $c_0$ and $c_1$ in the model $y = c_1 + c_0 sin(t)$, using least square approximation.

1 experiments with a periodic process gave the following data t 0 50 100 150 200 250 300 350 y 0754 1762 2041 1412 0303 0484 0380 0520 estimate the parameters c0 and c1 in the model y c1 49567

Added by Patricia J.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/18/2023

Step 1

This is done by solving the following system of equations: $\sum_{i=1}^{n} y_i = nc_1 + c_0 \sum_{i=1}^{n} sin(t_i)$ $\sum_{i=1}^{n} y_i sin(t_i) = c_1 \sum_{i=1}^{n} sin(t_i) + c_0 \sum_{i=1}^{n} sin^2(t_i)$ where $n$ is the number of data points. Show more…

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1. Experiments with a periodic process gave the following data: $t$: 0 50 100 150 200 250 300 350 $y$: 0.754 1.762 2.041 1.412 0.303 -0.484 -0.380 0.520 Estimate the parameters $c_0$ and $c_1$ in the model $y = c_1 + c_0 sin(t)$, using least square approximation.