In this exercise, you must write some scripts to‘complete’a program. You are provided with a filemaster.mand you must write the two filesrandXY.mandfindSlope.m. Themaster.mfile needs to accomplish two...

In this exercise, you must write some scripts to‘complete’a program. You are provided with a filemaster.mand you must write the two filesrandXY.mandfindSlope.m.

Themaster.mfile needs to accomplish two goals:

1. 
   

   a) generate some random data as part of a simulation

   
   


2. 
   

   b) identify the slope of that data.

   
   

We will use this to demonstrate how even simulated data with simulated noise can be difficult to analyse.

Themaster.mfile calls on the two filesrandXY.mandfindSlope.m. You must write these two files from scratch. Each file should only be a few lines long and define an appropriate function. The task that each file must accomplish is described as follows:

randXY.m

This file should define a function that takes one argument,N, which is length of vectors that will be returned. It will generate a random set of data withxspaced from 0 to 1 (taken from a uniform random distribution) andy = 5*x + 3with additional noise (taken from a normal distribution with a standard deviation of2). You should use the functionsrandandrandn.

findSlope.m

This file should define a function that takes two arguments, the vectorsxandy. It will then find the least-squares slope of the line of best fit for this data and return this value. You should use the functionpolyfit.

Note:the functionrngis called at the start of themaster.mscript. This should make the‘random’results the same for each run of the code. So long as you generate the random values in the same order as the solution, you will obtain the same results as indicated in the comments in the code.

Marking scheme

You are required to write two function files: randXY.m and findSlope.m. Each function file is worth 5 marks. 1 mark for each item listed below. randXY.m

• 
  

  Function is structuredcorrectly (includes “function” and “end”)

  
  


• 
  

  One input: N

  
  


• 
  

  Two outputs: x and y

  
  


• 
  

  Random numbers, uniformly distributed: x = rand(N,1);

  
  


• 
  

  Random numbers, normally distributed: y = 5*x + 3 + 2*randn(N,1) findSlope.m

  
  

• 
  

  Function is structured correctly (includes “function” and “end”)

  
  


• 
  

  Two inputs: x and y

  
  


• 
  

  One output: slope

  
  


• 
  

  Calculate coefficients: coeffs = polyfit(x,y,1);

  
  


• 
  

  Slope equals first coefficient: slope = coeffs(1);