Matlab and Root Mean Square help

[ndnbolla]

Matlab and Root Mean Square help please...

So I have this given data:

year = [1928:4:1936 1948:4:1956 1964:4:2000];

time = [12.2 11.9 11.5 11.9 11.5 11.5 11.4 11.08 11.07 11.08 11.06 10.97 10.54 10.82 10.94 10.75];

and after plotting it (time vs. year), I am told to find the best first order least squares fit to the data by a line using the polyfit function.

I am then told to find the root mean square error in this line and then plotting that best line?

How would I go about doing this?

When I did this, I used the function Fit1=polyfit(year, time, 1);

Fit1 came out to equal -0.0185 47.6837 which, when plotted on the same graph as the original data resembled nothing like it.

What am I doing wrong?

 

[abercrombiems02]

You did everything right, you probably just didnt interpret the answer right

Fit1 is a vector of the polynomial coefficient in descending order

In this case its telling you the best linear fit for the data is
time = -0.0185*year + 47.6837

One easy way of plotting this thing would be to plot your old data first and then make a new time vector corresponding to the linear fit

timefit = Fit1(1)*year + Fit1(2);

hold on;
plot(yearvect,timevect,'g')

This will plot the linear fit over the original data in green

To find the standard deviation we need to sum up the squares of the differences from the linear fit to the actual data, and then take the square root of all that junk.

for n = 1:length(year)
vect_error(n) = abs(time(n)^2 - timevect(n)^2);
end

stan_dev = sqrt(sum(vect_error));

(I get 6.7437 for the standard deviation - which seems reasonable from the plot of the two when comparing)

 

[tacman]

First of all, great job on using the polyfit function to find the best first order least squares fit for the given data. However, it seems like you may have made a small mistake in plotting the line.

To plot the best fit line, you can use the polyval function with the coefficients obtained from the polyfit function. So in this case, it would be something like y_fit = polyval(Fit1, year).

Now, to calculate the root mean square error (RMSE), you can use the following steps:
1. Calculate the residuals (difference between the actual data points and the predicted values from the best fit line), i.e. res = time - y_fit.
2. Square each residual value, i.e. res_squared = res.^2.
3. Take the mean of the squared residuals, i.e. mean_res_squared = mean(res_squared).
4. Finally, take the square root of the mean squared residuals to get the RMSE, i.e. RMSE = sqrt(mean_res_squared).

This will give you the RMSE for the best fit line. You can then plot this line along with the original data points to see how well it fits.

Hope this helps!