# maths using Matlab

Humidity influences evaporation, as a result, the solvent balance of water-reducible paints during sprayout is affected by humidity. A study is conducted to examine the relationship between % humidity (X) and solvent evaporation by % weight (Y ). Summary statistics for the data are:
x = 1314.90 y = 235.70 xy = 11,824.44 x2 = 76,308.53 y2 = 2286.07 n = 25
Using these summary statistics:

Find the least-squares estimates βˆ0 and βˆ1.

Compute the 95% confidence intervals for β0 and β1.

Perform a α = 0.05 hypothesis test to determine if solvent evaporation is af- fected by humidity.

Compute the R2 for the least-squares line and comment on the results.

Data are located in the file spraydata.csv . Use MATLAB to plot the data and the fitted least-squares. Use fitlm() in MATLAB to perform the tasks and provide a printout of your results, comment on the differences between the results obtained using the summary statistics and those obtained via MATLAB.
Limit the assessment to TWO A4 sized pages, using 12pt font, and margins no smaller than 1 inch. The document should be formatted as a PDF file.

(spraydata.csv)

Relative Humidity,Solvent Evaporation
35.3,11.0
29.7,11.1
30.8,12.5
58.8,8.4
61.4,9.3
71.3,8.7
74.4,6.4
76.7,8.5
70.7,7.8
57.5,9.1
46.4,8.2
28.9,12.2
28.1,11.9
39.1,9.6
46.8,10.9
48.5,9.6
59.3,10.1
70.0,8.1
70.0,6.8
74.4,8.9
72.1,7.7
58.1,8.5
44.6,8.9
33.4,10.4
28.6,11.1

assessment 2

Referring to the Week 11 Workshop and the spraydata.csv file, in MATLAB perform the linear regression as follows:

Import the data from spraydata.csv

Create the X matrix and y vector.

Solve for the least squares estimate β.

Compare your results to those obtained in the Week 11 Workshop using the summary statistics and those obtained using fitlm() in MATLAB.

Be sure to include your functioning MATLAB code and the resultant output. Con- sider the system of first-order ODE’s:
y1′ =5y2−y1+y3, y2′ =3y1−y2+t2, y3′ =y3−ty2.

Write out explicitly the matrix-vector representation of this system
y(t+h) ≈ Fy(t)+g. Clearly define the elements of y′, y, F , and g.

Write an algorithm describing how this would be implemented to solve for y(t) given h and y(0).

Implement this algorithm in MATLAB to solve for y(1) given h = 0.1 and y(0) = (0, 0, 0)′.

Plot the results for y1, y2, and y3 versus time.
Limit the assessment to TWO A4 sized pages, using 12pt font, and margins
no smaller than 1 inch. The document should be formatted as a PDF file.

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